In Greek, the words “Jew”, “Jews” and “Jewish” (sometimes translated “Judean”) are all variations on Ioudaios. That term was discussed in what some might call excruciating detail in the second post in this series, the length being necessary because of confusion arising from the way “Jew” is used today in popular secular and religious parlance.
Unsaved folk often refer to Gentiles converted to Judaism as “Jews”. This is most likely an accidental byproduct of unfamiliarity with biblical usage and/or the preferences of actual Jews, as opposed to evidence of a hidden agenda. Real Jews draw a clear distinction between their fellow Jews and converts to Judaism, whom they call proselytes. (Certain well-known evangelicals also use “Jew” to describe Gentiles, but for very specific theological reasons we won’t get into today.)
Suffice it to say that the Bible doesn’t use “Jew” that way.