sacredbible.org/
In the early Church, the Vulgate (the commonly used or widely used edition) was the Greek. Eventually, Latin became the most commonly used language for Bible texts. Prior to Jerome, there were very many different Latin editions of the various books. Jerome did much work to reduce these to fewer editions.
After Jerome, the number of editions, mostly edits of his work, increased.
The 1590 Pope Sixtus V edition sought to make a standard edition of the Bible in Latin, in accord with the decision of Trent to give the Latin Scriptural tradition a special place in the Scriptural life of the Church. This was revised under Pope Clement VIII in 1592, 93, and 98. the 98 edition was the standard Latin edition for many years, available in a number of scholarly edits.
The Neo-Vulgate was approved in 1979 as the typica (standard or reference) edition.
To answer the original question, there are versions of the Bible in Latin, and then there are edits (minor changes to a version). At some times in the history of the Church, the distinction between version and edition has not been clear.
Prior to Jerome there was no standard Latin Vulgate, but many different versions/editions (no clear distinction between versions and editions at that time) and none of these are extant. These are summed up in the phrase vetus latina
Versions:
vetus latina - not extant; numerous versions/editions
Jerome’s Vulgate - not extant
Since we don’t have Jerome’s work as a reference, it is difficult to know if subsequent editions were a new version (very different from past editions) or merely an edit of Jerome’s work.
Sixtine version - did not enter general useage, since it was soon revised by Clement VIII
Clementine version - available in numerous edits
Stuttgart version - NOT an edit of the Vulgate, but a Protestant work; should probably not be called Vulgate since it is not an edit of a commonly used Latin verison of the Bible
Tweedale (2005) - an edit of the Clementine Vulgate