Your problem stems from the inconsistent use of this word in the Torah itself. Compare:
Num 35:31 - premeditated murder:
"וְלֹא־תִקְחוּ כֹפֶר לְנֶפֶשׁ רֹצֵחַ אֲשֶׁר־הוּא רָשָׁע לָמוּת כִּי־מוֹת יוּמָת׃
You may not accept a ransom for the life of a murderer who is guilty of a capital crime; he must be put to death.
Num 35:11 - unintentional murder:
וְהִקְרִיתֶם לָכֶם עָרִים עָרֵי מִקְלָט תִּהְיֶינָה לָכֶם וְנָס שָׁמָּה רֹצֵחַ מַכֵּה־נֶפֶשׁ בִּשְׁגָגָה׃
You shall provide yourselves with places to serve you as cities of refuge to which a manslayer who has killed a person unintentionally may flee.
As you can see the term רצח is used both in intentional and unintentional cases, hence the problem with translating. As לא תרצח in the Torah text has no connotation, unlike the aforementioned verses, the translator must decide what to use.
Interestingly, the Hebrew word להרוג (kill) is also used interchangeably for a murder or a killing. So both are not precise definitions, sorry.