> Branches are pointers to a commit and that pointer is refreshed when a new commit is created. One could say they are a wandering tag (without explaining a tag for now).

A good name for these "wandering tags" would be "heads", since it's what git calls them internally (for instance, when not packed, they're stored at the "refs/heads/" path in the repository). This also exposes a distinction between a "branch" and its "head", and that distinction can be useful.