Matthew 5:21-32 is the best comment on these two verses.

Thou shalt not kill - This commandment, which is general, prohibits murder of every kind.

1. All actions by which the lives of our fellow creatures may be abridged.

2. All wars for extending empire, commerce, etc.

3. All sanguinary laws, by the operation of which the lives of men may be taken away for offenses of comparatively trifling demerit.

4. All bad dispositions which lead men to wish evil to, or meditate mischief against, one another; for, says the Scripture, He that hateth his brother in his heart is a murderer.

5. All want of charity to the helpless and distressed; for he who has it in his power to save the life of another by a timely application of succor, food, raiment, etc., and does not do it, and the life of the person either falls or is abridged on this account, is in the sight of God a murderer. He who neglects to save life is, according to an incontrovertible maxim in law, the same as he who takes it away.

6. All riot and excess, all drunkenness and gluttony, all inactivity and slothfulness, and all superstitious mortifications and self-denials, by which life may be destroyed or shortened; all these are point-blank sins against the sixth commandment.

Thou shalt not kill. Not meaning any sort of creatures, for there are some to be killed for the food and nourishment of men, and others for their safety and preservation; but rational creatures, men, women, and children, any of the human species, of every age, sex, condition, or nation; no man has a right to take away his own life, or the life of another; by this law is forbidden suicide, or self-murder, parricide or murder of parents, homicide or the murder of man; yet killing of men in lawful war, or in defence of a man's self, when his own life is in danger, or the execution of malefactors by the hands or order of the civil magistrate, and killing a man at unawares, without any design, are not to be reckoned breaches of this law; but taking away the life of another through private malice and revenge, and even stabbing of a man's character, and so all things tending to or designed for the taking away of life, and all plots, conspiracies, and contrivances for that purpose, even all sinful anger, undue wrath and envy, rancour of all mind, all malice in thought, word, or deed, are contrary to this precept, see Matthew 5:21 and which, on the other hand, requires that men should do all they can for the ease, peace, and preservation of the lives of men: this is the sixth command, but, in the Septuagint, the strict order in which this and the two following precepts lie is not observed, rehearsing them thus, "thou shall not commit adultery, thou shall not steal, thou shall not kill"; and so in Mark 10:19 the order is inverted.

The other Five Words or commandments, which determine the duties to one's neighbour, are summed up in Leviticus 19:18 in the one word, "Love thy neighbour as thyself." The order in which they follow one another is the following: they first of all secure life, marriage, and property against active invasion or attack, and then, proceeding from deed to word and thought, they forbid false witness and coveting.

(Note: Luther has pointed out this mirum et aptum ordinem, and expounds it thus: Incipit prohibitio a majori usque ad minimum, nam maximum damnum est occisio hominis, deinde proximum violatio conjugis, tertium ablatio facultatis. Quod qui in iis nocere non possunt, saltem lingua nocent, ideo quartum est laesio famae. Quodsi in iis non praevalent omnibus, saltem corde laedunt proximum, cupiendo quae ejus sunt, in quo et invidia proprie consistit.)

If, therefore, the first three commandments in this table refer primarily to deeds; the subsequent advance to the prohibition of desire is a proof that the deed is not to be separated from the disposition, and that "the fulfilment of the law is only complete when the heart itself is sanctified" (Oehler). Accordingly, in the command, "Thou shalt not kill," not only is the accomplished fact of murder condemned, whether it proceed from open violence or stratagem (Exodus 21:12, Exodus 21:14, Exodus 21:18), but every act that endangers human life, whether it arise from carelessness (Deuteronomy 22:8) or wantonness (Leviticus 19:14), or from hatred, anger, and revenge (Leviticus 19:17-18). Life is placed at the head of these commandments, not as being the highest earthly possession, but because it is the basis of human existence, and in the life the personality is attacked, and in that the image of God (Genesis 9:6). The omission of the object still remains to be noticed, as showing that the prohibition includes not only the killing of a fellow-man, but the destruction of one's own life, or suicide. - The two following commandments are couched in equally general terms. Adultery, נאף, which is used in Leviticus 20:10 of both man and woman, signifies (as distinguished from זנה to commit fornication) the sexual intercourse of a husband with the wife of another, or of a wife with the husband of another. This prohibition is not only directed against any assault upon the husband's dearest possession, for the tenth commandment guards against that, but upholds the sacredness of marriage as the divine appointment for the propagation and multiplication of the human race; and although addressed primarily to the man, like all the commandments that were given to the whole nation, applies quite as much to the woman as to the man, just as we find in Leviticus 20:10 that adultery was to be punished with death in the case of both the man and the woman. - Property was to be equally inviolable. The command, "Thou shalt not steal," prohibited not only the secret or open removal of another person's property, but injury done to it, or fraudulent retention of it, through carelessness or indifference (Exodus 21:33; Exodus 22:13; Exodus 23:4-5; Deuteronomy 22:1-4). - But lest these commandments should be understood as relating merely to the outward act as such, as they were by the Pharisees, in opposition to whom Christ set forth their true fulfilment (Matthew 5:21.), God added the further prohibition, "Thou shalt not answer as a false witness against thy neighbour," i.e., give false testimony against him. ענה and בּ: to answer or give evidence against a person (Genesis 30:33). עד is not evidence, but a witness. Instead of שׁקר עד, a witness of a lie, who consciously gives utterance to falsehood, we find שׁוא עד in Deuteronomy, one who says what is vain, worthless, unfounded (שׁוא שׁמע, Exodus 23:1; on שׁוא see Exodus 23:7). From this it is evident, that not only is lying prohibited, but false and unfounded evidence in general; and not only evidence before a judge, but false evidence of every kind, by which (according to the context) the life, married relation, or property of a neighbour might be endangered (cf. Exodus 23:1; Numbers 35:30; Deuteronomy 17:6; Deuteronomy 19:15; Deuteronomy 22:13.). - The last or tenth commandment is directed against desiring (coveting), as the root from which every sin against a neighbour springs, whether it be in word or deed. The חמד, ἐπιθυμεῖν (lxx), coveting, proceeds from the heart (Proverbs 6:25), and brings forth sin, which "is finished" in the act (James 1:14-15). The repetition of the words, "Thou shalt not covet," does not prove that there are two different commandments, any more than the substitution of תּתאוּה in Deuteronomy 5:18 for the second תּחמד. חמד and התאוּה are synonyms, - the only difference between them being, that "the former denotes the desire as founded upon the perception of beauty, and therefore excited from without, the latter, desire originating at the very outset in the person himself, and arising from his own want or inclination" (Schultz). The repetition merely serves to strengthen and give the great emphasis to that which constitutes the very kernel of the command, and is just as much in harmony with the simple and appropriate language of the law, as the employment of a synonym in the place of the repetition of the same word is with the rhetorical character of Deuteronomy. Moreover, the objects of desire do not point to two different commandments. This is evident at once from the transposition of the house and wife in Deuteronomy. בּית (the house) is not merely the dwelling, but the entire household (as in Genesis 15:2; Job 8:15), either including the wife, or exclusive of her. In the text before us she is included; in Deuteronomy she is not, but is placed first as the crown of the man, and a possession more costly than pearls (Proverbs 12:4; Proverbs 31:10). In this case, the idea of the "house" is restricted to the other property belonging to the domestic economy, which is classified in Deuteronomy as fields, servants, cattle, and whatever else a man may have; whereas in Exodus the "house" is divided into wife, servants, cattle, and the rest of the possessions.

Thou shalt not {i} kill.

(i) But love and preserve your brother's life.

20:13 Thou shalt not kill - Thou shalt not do any thing hurtful to the health, or life of thy own body, or any other's. This doth not forbid our own necessary defence, or the magistrates putting offenders to death; but it forbids all malice and hatred to any, for he that hateth his brother is a murderer, and all revenge arising therefrom; likewise anger and hurt said or done, or aimed to be done in a passion; of this our Saviour expounds this commandment, Mt 5:22.

20:12-17 The laws of the SECOND table, that is, the last six of the ten commandments, state our duty to ourselves and to one another, and explain the great commandment, Thou shalt love thy neighbour as thyself, Lu 10:27. Godliness and honesty must go together. The fifth commandment concerns the duties we owe to our relations. Honour thy father and thy mother, includes esteem of them, shown in our conduct; obedience to their lawful commands; come when they call you, go where they send you, do what they bid you, refrain from what they forbid you; and this, as children, cheerfully, and from a principle of love. Also submission to their counsels and corrections. Endeavouring, in every thing, to comfort parents, and to make their old age easy; maintaining them if they need support, which our Saviour makes to be particularly intended in this commandment, Mt 15:4-6. Careful observers have noted a peculiar blessing in temporal things on obedient, and the reverse on disobedient children. The sixth commandment requires that we regard the life and the safety of others as we do our own. Magistrates and their officers, and witnesses testifying the truth, do not break this command. Self-defence is lawful; but much which is not deemed murder by the laws of man, is such before God. Furious passions, stirred up by anger or by drunkenness, are no excuse: more guilty is murder in duels, which is a horrible effect of a haughty, revengeful spirit. All fighting, whether for wages, for renown, or out of anger and malice, breaks this command, and the bloodshed therein is murder. To tempt men to vice and crimes which shorten life, may be included. Misconduct, such as may break the heart, or shorten the lives of parents, wives, or other relatives, is a breach of this command. This command forbids all envy, malice, hatred, or anger, all provoking or insulting language. The destruction of our own lives is here forbidden. This commandment requires a spirit of kindness, longsuffering, and forgiveness. The seventh commandment concerns chastity. We should be as much afraid of that which defiles the body, as of that which destroys it. Whatever tends to pollute the imagination, or to raise the passions, falls under this law, as impure pictures, books, conversation, or any other like matters. The eighth commandment is the law of love as it respects the property of others. The portion of worldly things allotted us, as far as it is obtained in an honest way, is the bread which God hath given us; for that we ought to be thankful, to be contented with it, and, in the use of lawful means, to trust Providence for the future. Imposing upon the ignorance, easiness, or necessity of others, and many other things, break God's law, though scarcely blamed in society. Plunderers of kingdoms though above human justice, will be included in this sentence. Defrauding the public, contracting debts without prospect of paying them, or evading payment of just debts, extravagance, all living upon charity when not needful, all squeezing the poor in their wages; these, and such things, break this command; which requires industry, frugality, and content, and to do to others, about worldly property, as we would they should do to us. The ninth commandment concerns our own and our neighbour's good name. This forbids speaking falsely on any matter, lying, equivocating, and any way devising or designing to deceive our neighbour. Speaking unjustly against our neighbour, to hurt his reputation. Bearing false witness against him, or in common conversation slandering, backbiting, and tale-bearing; making what is done amiss, worse than it is, and in any way endeavouring to raise our reputation upon the ruin of our neighbour's. How much this command is every day broken among persons of all ranks! The tenth commandment strikes at the root; Thou shalt not covet. The others forbid all desire of doing what will be an injury to our neighbour; this forbids all wrong desire of having what will gratify ourselves.