כֵּיצַד מְאַיְּמִין אֶת הָעֵדִים עַל עֵדֵי נְפָשׁוֹת, הָיוּ מַכְנִיסִין אוֹתָן וּמְאַיְּמִין עֲלֵיהֶן. שֶׁמָּא תֹאמְרוּ מֵאֹמֶד, וּמִשְּׁמוּעָה, עֵד מִפִּי עֵד וּמִפִּי אָדָם נֶאֱמָן שָׁמַעְנוּ, אוֹ שֶׁמָּא אִי אַתֶּם יוֹדְעִין שֶׁסּוֹפֵנוּ לִבְדֹּק אֶתְכֶם בִּדְרִישָׁה וּבַחֲקִירָה. הֱווּ יוֹדְעִין שֶׁלֹּא כְדִינֵי מָמוֹנוֹת דִּינֵי נְפָשׁוֹת. דִּינֵי מָמוֹנוֹת, אָדָם נוֹתֵן מָמוֹן וּמִתְכַּפֵּר לוֹ. דִּינֵי נְפָשׁוֹת, דָּמוֹ וְדַם זַרְעִיּוֹתָיו תְּלוּיִין בּוֹ עַד סוֹף הָעוֹלָם, שֶׁכֵּן מָצִינוּ בְקַיִן שֶׁהָרַג אֶת אָחִיו, שֶׁנֶּאֱמַר (בראשית ד) דְּמֵי אָחִיךָ צֹעֲקִים, אֵינוֹ אוֹמֵר דַּם אָחִיךָ אֶלָּא דְּמֵי אָחִיךָ, דָּמוֹ וְדַם זַרְעִיּוֹתָיו. דָּבָר אַחֵר, דְּמֵי אָחִיךָ, שֶׁהָיָה דָמוֹ מֻשְׁלָךְ עַל הָעֵצִים וְעַל הָאֲבָנִים. לְפִיכָךְ נִבְרָא אָדָם יְחִידִי, לְלַמֶּדְךָ, שֶׁכָּל הַמְאַבֵּד נֶפֶשׁ אַחַת מִיִּשְׂרָאֵל, מַעֲלֶה עָלָיו הַכָּתוּב כְּאִלּוּ אִבֵּד עוֹלָם מָלֵא. וְכָל הַמְקַיֵּם נֶפֶשׁ אַחַת מִיִּשְׂרָאֵל, מַעֲלֶה עָלָיו הַכָּתוּב כְּאִלּוּ קִיֵּם עוֹלָם מָלֵא. וּמִפְּנֵי שְׁלוֹם הַבְּרִיּוֹת, שֶׁלֹּא יֹאמַר אָדָם לַחֲבֵרוֹ אַבָּא גָדוֹל מֵאָבִיךָ. וְשֶׁלֹּא יְהוּ מִינִין אוֹמְרִים, הַרְבֵּה רָשֻׁיּוֹת בַּשָּׁמָיִם. וּלְהַגִּיד גְּדֻלָּתוֹ שֶׁל הַקָּדוֹשׁ בָּרוּךְ הוּא, שֶׁאָדָם טוֹבֵעַ כַּמָּה מַטְבְּעוֹת בְּחוֹתָם אֶחָד וְכֻלָּן דּוֹמִין זֶה לָזֶה, וּמֶלֶךְ מַלְכֵי הַמְּלָכִים הַקָּדוֹשׁ בָּרוּךְ הוּא טָבַע כָּל אָדָם בְּחוֹתָמוֹ שֶׁל אָדָם הָרִאשׁוֹן וְאֵין אֶחָד מֵהֶן דּוֹמֶה לַחֲבֵרוֹ. לְפִיכָךְ כָּל אֶחָד וְאֶחָד חַיָּב לוֹמַר, בִּשְׁבִילִי נִבְרָא הָעוֹלָם. וְשֶׁמָּא תֹאמְרוּ מַה לָּנוּ וְלַצָּרָה הַזֹּאת, וַהֲלֹא כְבָר נֶאֱמַר (ויקרא ה) וְהוּא עֵד אוֹ רָאָה אוֹ יָדָע אִם לוֹא יַגִּיד וְגוֹ'. וְשֶׁמָּא תֹאמְרוּ מַה לָּנוּ לָחוּב בְּדָמוֹ שֶׁל זֶה, וַהֲלֹא כְבָר נֶאֱמַר (משלי יא) וּבַאֲבֹד רְשָׁעִים רִנָּה:
How do they instill fear [into the witnesses] in capital cases? They would bring them in and instill fear in them, [saying:] Lest you [offer testimony that includes] inductive inference, rumor, [information heard] from another witness, [or claim,] 'we heard [this] from a trustworthy individual,' or lest you did not know that we will interrogate you with cross-examination; you should know that capital cases are unlike monetary cases. [In] monetary cases, an individual pays money and attains atonement. [However, in] capital cases, [the accused's] blood and the blood of his [potential] offspring until eternity are dependent on [the case's outcome]. For thus do we find with respect to Cain, who killed his brother, as it says, (Bereshit 4:10) "the bloods of your brother call out"; it does not say "the blood of your brother," but rather "the bloods of your brother"- his blood and the blood of his [potential] offspring. Another explanation [of the plural form]: "the bloods of your brother"- for his blood was splattered cast upon the trees and rocks. It was for this reason that man was created unique, to teach you that anyone who destroys one life from the Jewish people is considered by Scripture to have destroyed an entire world; and anyone who saves one life from the Jewish people is as if he saved an entire world. And also, to promote peace among people, that no one will say to his fellow, "My ancestors are greater than yours." And also, so that sectarians will not say, "There are many powers in Heaven." And also, to express the grandeur of The Holy One blessed be He: For a man strikes many coins from the same die, and all the coins are alike; whereas the King, the King of Kings, The Holy One blessed be He struck every man from the die of the First Man [Adam], and yet no man is quite like his fellow. Therefore, every person is obligated to say, "For me the world was created." And lest you say, "Why must we go through all this trouble?" has it not already been said (Vayikra 5:1), "he being a witness, whether he has seen or known, if he do not utter it, etc." And lest you say, "Why must we [testify and thereby] be responsible for the [loss] of this person's life? has it not already been said, (Mishlei 11:10) "And when the wicked perish, there is joy."
שכל המאבד נפש אחת מעלין עליו כאילו איבד עולם מלא וכל המקיים נפש אחת מעלין עליו כאילו קיים עולם מלא
Anyone who destroys one life is considered by Scripture to have destroyed an entire world; and anyone who saves one life is as if (they) saved an entire world.
Here the level of disagreement is nuanced, particularistic vs. universalist.
The Bavli [Sanhedrin 37a] does say "a Jewish life":
The Yerushalmi [Sanhedrin 4:1 (22a)] does not carry that phrase. Who wins? One statement is more specific, the other, universal.
שכל המאבד נפש אחת מישראל מעלה עליו הכתוב כאילו איבד עולם מלא וכל המקיים נפש אחת מישראל מעלה עליו הכתוב כאילו קיים עולם מלא ומפני שלום הבריות שלא יאמר אדם לחבירו אבא גדול מאביך ושלא יהו המינים אומרים הרבה רשויות בשמים ולהגיד גדולתו של הקב"ה שאדם טובע כמה מטבעות בחותם אחד כולן דומין זה לזה
anyone who destroys one soul from the Jewish people, the verse ascribes him blame as if he destroyed an entire world, as Adam was one person, from whom the population of an entire world came forth. And conversely, anyone who sustains one soul from the Jewish people, the verse ascribes him credit as if he sustained an entire world. The mishna cites another reason Adam the first man was created alone: And this was done due to the importance of maintaining peace among people, so that one person will not say to another: My father, i.e., progenitor, is greater than your father. And it was also so that the heretics who believe in multiple gods will not say: There are many authorities in Heaven, and each created a different person.