Earlier quoted context omitted.
The quote is kinda wrong in that point 1 and 2 are mixed up. Branches are just pointers to commits. Commits contain a reference to their history. It's only kind of incorrect because in praxis branches are used to refer to a history (a sequence of commits). But it's also misleading once you have to do anything more complicated than just commiting/merging. When I started out using git I was working with the same assump…
Do you have an actual example of this? I've never encountered a situation where those three points are incorrect.
[1] The main difference perhaps is that, if you create a new commit, the branch pointer will actually be moved to point to that latest commit (while tag stays fixed).