In Ezra 7:11, that Ezra is described as both priest and scribe. In Nehemiah 12:26, Ezra "the priestly scribe" [Hebrew: "the priest, the scribe"] is mentioned in conjunction with Nehemiah "the governor." These are some years after the time of Jeshua the High Priest and Zerubbabel.
If the Ezra from verse 26 differs from the Ezra of verse 1, the reader would expect the author to distinguish. Consistently, Ezra the from the book of Ezra is described as "the priest," "the scribe," or "the priestly scribe." The Ezra of Nehemiah 12:1 is distinguished by not having that description.
Regarding the Ezra of Nehemiah 12:26 and the book of Ezra, it would be logical to conclude that this priestly scribe is the same as "the priest, the scribe" of Ezra 7 and on.
There are questions among scholars if the priest Ezra of Nehemiah 12:1 is the same as the Ezra from the book of Ezra. Both Ezra and Nehemiah date their activities in the reign of King Artaxerxes but do not indicate if this is Artaxerxes I (465-424) or Artaxerxes II (404-359). Ezra writes he began his journey in Artaxerxes seventh year (7:7), and Nehemiah appeared before the king in the 20th (1:1). It is even possible, if one assumes a long life span for the first traveler, one was sent by Artaxerxes I and the other by Artaxerxes II. A good explanation of the problems and reconciliation can be read at BibleHub.
However, Ezra does not just suddenly appear in Nehemiah 12 as the statement from the Encyclopedia Britannica (quoted in the link) as Nehemiah and Ezra "seem to have no knowledge of each other; their missions do not overlap" implies. Nehemiah's Ezra first appears in Nehemiah 8, being asked to read the Torah to the congregation. This is very similar to the set of actions taken by Ezra the priest in Ezra 10.
Ezra and Nehemiah have traditionally been seen as contemporaries. Their two books were kept as a single scroll until the third century (when Christians separated the two) and the fifteenth (when Jews separated the two). The Septuagint has them as one book, and the final Masorah statistics appear only after Nehemiah and combine both books.
The conclusion that Ezra "the priest, the scribe" of Ezra is the same as the Ezra "the priest, the scribe" of Nehemiah is a natural reading of the text. The Ezra of Nehemiah 12:1, since not described as "the priest," "the scribe," or "priestly scribe" can be concluded to be different.