Good point, that is a bit of a quirk to the model. (Bloody useful, wouldn't have it another way obviously. But it is a special treatment more than 'a name for a commit'.)

I suppose I can recover by saying 'committing creates a new commit, with HEAD as parent, and updates the checked out pointer to point at it'. Where no branch, a 'detached HEAD', is perhaps more thr special case - it's a sort of nameless transparent pointer that updates but you're only aware of the commit ref itself. Although again tag is also a special case in that it doesn't update, as you say. Really they're just all different ways of referring to a commit, doesn't really make sense to call any one of them the true way and the others special cases.

I stand by the commit being the 'sequence of commits' though. So tldr, branches, tags, detached heads are just different mechanisms for referring to such a sequence: named and updates, named and static, unnamed/transparent. But in each case, they point to a commit, and inherently the sequence behind it.