The software for this is called 'git'. The general term for this family of software is "source control". There are many types of source control but git is massively popular.
All the changes are recorded in a "repository". At any time you can add your own changes to your repository or import changes others made to theirs. Git takes care of merging the changed files together and warning you of anything it couldn't merge because of conflicts. It's pretty magical.
Git was originally written by Linus, the guy who made the Linux kernel.
That should give you plenty to google!
For little snippets of CSS like user styles, git is probably overkill...?