Gerald L. Borchert (in John 1–11, vol. 25A, of The New American Commentary, page 126) identifies and summarizes well the adversarial nature of "the Jews" in the gospel of John.
The use of the term “Jews” here, as in most of the Gospel, belies
immediately an adversarial thrust to these persons. While there is an
affirmation at 4:22 that salvation is from the Jews, the major use of
the term “Jews” in this Gospel seems to be connected with officials of
the temple and synagogue. They are portrayed by the writer as the
opponents of Jesus.
It is fairly certain that "the Jews" must refer to a subset of Israelites, since there are many others, contrasted to them, who are ethnic Jews. For instance, Mary and Martha are Jewish, yet at the mourning of Lazarus' death, it is significant that some of "the Jews" were in attendance (John 11:19, 31, 33). Mary and Martha were distinct from "Jews" in that narrative.
Apparently, the term signified a social or religious status, a term to refer to the (self-styled?) "real" Jews - the serious ones. It can be likened to the term "Americans." All who live in the United States are 'Americans' but only a few were part of the "American" party in Utah in the early 1900's.
Another clue as to the identity of "the Jews" is that they somehow controlled who was allowed to participate in the synagogue and who was not (John 9:22).
What we can not do is simplify this by saying all Israelites who rejected Jesus were called Jews, and those who were open to him were not called Jews. That assumption would wreak havoc with the interpretation of John.
Now to the question. Were the "Jews" of John 10:19-21 the same group of people or a different group than the ones mentioned in 10:24-39?
There seem to be no contextual cues that the groups are different. It does appear that Jesus was able to speak in such a way to this hardened group, a group predisposed to reject him, that he convinced some to believe in him.
Even after "the Jews" as a group decided to oppose all who trusted in Jesus (John 9:22), some of their own had second thoughts (John 10:19-21), and some would even believe (John 12:45). But as a whole, they continued to oppose Jesus vehemently (John 10:24-39).