There are no real conventions, and people often take liberties. There are some that match up fairly well, like Sarah in English and Hebrew, and there are some that are close with a phonetically similar first initial, such as Michael and Moshe. There are also some that have some visual similarity, in that the transliteration of the Hebrew word commonly uses a letter that is then adopted as the starting point for choosing a name in the vernacular language, such as Shlomo and Steven/Stephen. Finally, there are those that use completely unrelated names, sometimes seizing the opportunity to give different additional names in honor or memory of additional people. I've seen this further developed into giving someone a vernacular name after a close friend or relative who was not Jewish or did not have a Hebrew name, and a Hebrew name for someone who was Jewish with a Hebrew name.
Note, also, that I'm using the word 'Hebrew' loosely; many times the "Jewish" name is not Hebrew at all, but Yiddish, Aramaic, or even Greek, Arabic, or Farsi.