I understand there is one Mishnah and two Talmuds (Bavli and Yerushalmi). But is the text of the Mishnah associated with each Talmud exactly the same? Rabbi Gil Student states that the famous quote about "saving one life is the same as saving a world" applies only to Jews only in the Bavli version, but in the Yerushalmi version it applies to everybody.
Wikipedia tells us, without a source, that:
Very roughly, there are two traditions of Mishnah text. One is found in manuscripts and printed editions of the Mishnah on its own, or as part of the Jerusalem Talmud. The other is found in manuscripts and editions of the Babylonian Talmud; though there is sometimes a difference between the text of a whole paragraph printed at the beginning of a discussion (which may be edited to conform with the text of the Mishnah-only editions) and the line-by-line citations in the course of the discussion.
Can somebody clarify the matter? If there are indeed recognized differences, is there a list of them somewhere?