The branch, like the tag, is a single reference to a commit.
Do this:
$ cat .git/refs/heads/mainThat said, it only makes sense to make such implicit mental shortcuts once you're already comfortable with git's data model. If you're not and you're still learning it, it's only going to confuse you.
The “dots on the line” visualization is pretty clear: you can have any number of branches pointing to a specific dot/commit. How do you add “branches” without fundamentally breaking that concept? When you create a branch, you’re not copying the line, you’re just adding a pointer.
(Also, note the path you ask us to cat does not contain the word "branch". You refer to how things are stored to support your definition, but the way things are stored doesn't use the term "branch".)
Plus that definition describes both tags and branches, how do you tell them apart? It’s clearly lacking. Actually that definition fits commits too.
I’d rather use these:
Branch: a pointer that advances
Tag: a permanent pointer
Commit/hash: an even more permanent pointer (because even a force can’t change it) that also describes the changes.