Is the "Versions and History" transferrable between instances of the program? Can it be reliably used by a couple, dozens, even hundreds of people?
Yes. Onshape is web based. Every change is tracked and can be rolled back. There are versions and branches. Multiple people can work on the same document. The equivalent of a git comment would be a version with a comment.
Version control and source control are interchangeable terms and they both refer to tracking changes, it doesn't have to be source code