Based upon an article in TheTorah.com by Prof. Rabbi Marty Lockshin
(א) לא תרצח - כל רציחה - הריגה בחנם היא בכל מקום. מות יומת הרוצח. אבל הריגה ומיתה יש בחנם כמו:... ויהרגהו דקין.
ויש בדין כמו: והרגת את האשה.
ומה שכתוב: אשר ירצח את רעהו בבלי דעת, לפי שמדבר בענין רוצח במזיד, לכך הוא אומר: ואם רציחה זו בבלי דעת פטור. [.See below]
זו תשובה שהשבתי לאפיקורסים והודו לי. ואף על פי שיש בספריהם אני אמית ואחיה בלשון לטי"ן של לא תרצח, הם לא דקדקו.
(French, d. 1158?)
(1) לא תרצח. Wherever the term רציחה appears it refers to killing without adequate justification. A deliberate murderer is to be executed as we know from Numbers 35:16-16.....
When the terms הריגה, or מיתה are used to describe killing this means that there was no excuse for the killer to commit his act. (compare Cain slaying his brother in Genesis 4:8)
On the other hand, in Leviticus 20,16 where the Torah decrees והרגת את האשה, this refers to judicial killing for cause. [bestiality]
Concerning the use of the word רוצח, murderer, in Deuteronomy 4:42 as applicable to someone who killed inadvertently, the reason why the Torah used this term there was only because in the same context deliberate murder was also discussed.
This is my answer to the heretics who have admitted to me that the Latin translation of the Bible describing רציחה “killing,” without distinction as to the reason for the killing, is sloppy, most inaccurate. They were so careless in spite of the fact that in their “own” books such as Deuteronomy 32,39 we have the line אני אמית ואחיה, “it is I Who kill and resurrect,” showing that the Torah uses different expressions describing different kinds of killing.
(א) לא תרצח
...רציחה מורטר"א (meurtre, Mord) בלע"ז והיא מיתה שלא כדין. ואין לשון רציחה שייך אלא בשלא כדין, אבל מיתה והריגה שייכי בין בדין בין שלא בדין כדכתיב במיתת בית דין, כי הרג תהרגנו, מות יומת, דמיו בו ולפיכך אין צריך כאן פי' אחר, כי לשון רציחה מוכיח שאינו מזהיר אלא על שלא כדין:
(French; pupil of Rashbam and others)
He states that the French picks up this distinction by using "meurtre," to murder, exclusively in unjustified cases, and מיתה והריגה, which can be used in justifiable homicide (in a court, for example) or unjustified.
("Meurtre" can be contrasted to "tuer" which means "to kill" without regard to justification.)
However, there are some verses that are not consistent with the Rashbam's distinction: Numbers 35: 11, 12, 27 and 30; Deuteronomy 4:42
(יא) וְהִקְרִיתֶ֤ם לָכֶם֙ עָרִ֔ים עָרֵ֥י מִקְלָ֖ט תִּהְיֶ֣ינָה לָכֶ֑ם וְנָ֥ס שָׁ֙מָּה֙ רֹצֵ֔חַ מַכֵּה־נֶ֖פֶשׁ בִּשְׁגָגָֽה׃ (יב) וְהָי֨וּ לָכֶ֧ם הֶעָרִ֛ים לְמִקְלָ֖ט מִגֹּאֵ֑ל וְלֹ֤א יָמוּת֙ הָרֹצֵ֔חַ עַד־עׇמְד֛וֹ לִפְנֵ֥י הָעֵדָ֖ה לַמִּשְׁפָּֽט....
(כב) וְאִם־בְּפֶ֥תַע בְּלֹא־אֵיבָ֖ה הֲדָפ֑וֹ אוֹ־הִשְׁלִ֥יךְ עָלָ֛יו כׇּל־כְּלִ֖י בְּלֹ֥א צְדִיָּֽה׃ (כג) א֣וֹ בְכׇל־אֶ֜בֶן אֲשֶׁר־יָמ֥וּת בָּהּ֙ בְּלֹ֣א רְא֔וֹת וַיַּפֵּ֥ל עָלָ֖יו וַיָּמֹ֑ת וְהוּא֙ לֹא־אוֹיֵ֣ב ל֔וֹ וְלֹ֥א מְבַקֵּ֖שׁ רָעָתֽוֹ׃ (כד) וְשָֽׁפְטוּ֙ הָֽעֵדָ֔ה בֵּ֚ין הַמַּכֶּ֔ה וּבֵ֖ין גֹּאֵ֣ל הַדָּ֑ם עַ֥ל הַמִּשְׁפָּטִ֖ים הָאֵֽלֶּה׃ (כה) וְהִצִּ֨ילוּ הָעֵדָ֜ה אֶת־הָרֹצֵ֗חַ מִיַּד֮ גֹּאֵ֣ל הַדָּם֒ וְהֵשִׁ֤יבוּ אֹתוֹ֙ הָֽעֵדָ֔ה אֶל־עִ֥יר מִקְלָט֖וֹ אֲשֶׁר־נָ֣ס שָׁ֑מָּה וְיָ֣שַׁב בָּ֗הּ עַד־מוֹת֙ הַכֹּהֵ֣ן הַגָּדֹ֔ל אֲשֶׁר־מָשַׁ֥ח אֹת֖וֹ בְּשֶׁ֥מֶן הַקֹּֽדֶשׁ׃ (כו) וְאִם־יָצֹ֥א יֵצֵ֖א הָרֹצֵ֑חַ אֶת־גְּבוּל֙ עִ֣יר מִקְלָט֔וֹ אֲשֶׁ֥ר יָנ֖וּס שָֽׁמָּה׃
(ל) כׇּ֨ל־מַכֵּה־נֶ֔פֶשׁ לְפִ֣י עֵדִ֔ים יִרְצַ֖ח אֶת־הָרֹצֵ֑חַ וְעֵ֣ד אֶחָ֔ד לֹא־יַעֲנֶ֥ה בְנֶ֖פֶשׁ לָמֽוּת׃
(11) you shall provide yourselves with places to serve you as cities of refuge to which [a man] who has killed someone —who has slain a person unintentionally—may flee. (12) The cities shall serve you as a refuge from the avenger, so that the killer may not die unless he has stood trial before the assembly....
(22) But if [a man] pushed without malice aforethought or hurled any object at [the victim] unintentionally, (23) or inadvertently dropped upon [the victim] any deadly object of stone, and death resulted—though not being an enemy and not seeking to harm— (24) in such cases the assembly shall decide between the slayer and the blood-avenger. (25) The assembly shall protect the killer from the blood-avenger, and the assembly shall restore him to the city of refuge to which he fled, and there he shall remain until the death of the high priest who was anointed with the sacred oil. (26) But if the killer ever goes outside the limits of the city of refuge to which he has fled....
(30) If anyone slays a person, the killer may be executed only on the evidence of witnesses; the testimony of a single witness against a person shall not suffice for a sentence of death.
Prof. Gerald Blidstein (Judaism 14, 1965) noted that NJPS used four different translations for the root רֹצֵ֗חַ - "murder," "kill," "manslayer," and "execute."
[CS: Note: there are various contexts when killing is permitted, or even mandated, such as in self-defense or as a punishment. (If one does not defend oneself in the case of a clear life-threatening attack, is that an act of suicide?)]
Blidstein states that, in contrast to Christianity, Judaism is a "...realistic, hard-headed system, committed to a law of justice rather than a chaos of love. An obvious line is being drawn between a faith that reads, "You shall not murder," and one that naively and unrealistically demands, "You shall not kill."
He argues that the usage of various terminologies in Humash might be intentionally and reflective of Judaism's values regarding the taking of life.
(י)....סַנְהֶדְרִין נוֹהֶגֶת בָּאָרֶץ וּבְחוּצָה לָאָרֶץ.
סַנְהֶדְרִין הַהוֹרֶגֶת אֶחָד בְּשָׁבוּעַ נִקְרֵאת חָבְלָנִית.
רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה אוֹמֵר, אֶחָד לְשִׁבְעִים שָׁנָה.
רַבִּי טַרְפוֹן וְרַבִּי עֲקִיבָא אוֹמְרִים, אִלּוּ הָיִינוּ בַסַּנְהֶדְרִין לֹא נֶהֱרַג אָדָם מֵעוֹלָם. רַבָּן שִׁמְעוֹן בֶּן גַּמְלִיאֵל אוֹמֵר, אַף הֵן מַרְבִּין שׁוֹפְכֵי דָמִים בְּיִשְׂרָאֵל:
(10)....The mitzva to establish a Sanhedrin with the authority to administer capital punishments is in effect both in Eretz Yisrael and outside Eretz Yisrael.
A Sanhedrin that executes a transgressor once in seven years is characterized as a destructive tribunal. Since the Sanhedrin would subject the testimony to exacting scrutiny, it was extremely rare for a defendant to be executed.
Rabbi Elazar ben Azarya says: This categorization applies to a Sanhedrin that executes a transgressor once in seventy years.
Rabbi Tarfon and Rabbi Akiva say: If we had been members of the Sanhedrin, we would have conducted trials in a manner whereby no person would have ever been executed.
Rabban Shimon ben Gamliel says: In adopting that approach, they too would increase the number of murderers among the Jewish people. The death penalty would lose its deterrent value, as all potential murderers would know that no one is ever executed.
Blidstein writes: "No word for the spilling of human blood could bear a less prohibitive denotation than any other.... Western thought distinguishes, at a basic and indelible level...between homicide and murder. Jewish usage does not make this distinctin. The verbal integrity of the spilling of human blood is never violated; homicide is not splintered into the justifiable and the criminal."
Lockshin concludes his article: "...we could say with Blidstein, that the lack of clarity of the root רֹצֵ֗חַ is meant to teach us to abhor all killing of human beings."