Then the word would be the same in the Hebrew [Hebraisti], the Aramaic [Syriac], and the Chaldean [Chaldaios] like some words are and some words aren't.
Well, the Greeks say Hebraisti is Chaldee and the Jews say they spoke Aramaic. I believe tboth becuase it is about their langue. The Latins obviously translated it incorrectly, and through the Latins the error spread throughout the west.
In Greek, Ioudaisti is (OT) Hebrew. Ioudiasti is not used in the NT. It is perhaps unfortunate that they called Chaldee Hebraisti because they should have known there would be obtuse literalist translators who will create confusion and heresy in the west.