What's stopping us from just using those words to describe operations with Git?
I mean, what Git is, is a data structure with a set of operations on it, and the design of that is pretty fundamental at this point. We'd need to see something more novel[1].
(Sidenote: Git almost seemed an obvious trajectory for version control given how problematic file-based approaches have been. I've used far too many version control systems, including "ancient" awful ones like Harvest[2], and it just felt inevitable that we'd one day rely on an "always-branching" model.)
[1]: I did think of something more novel: semantic version control (https://news.ycombinator.com/item?id=25537455)
[2]: https://en.wikipedia.org/wiki/CA_Harvest_Software_Change_Man...