Terminology question about remote branches.

I am trying to dig through man-pages and user manual and trying to match them with reality. I seem to have a hard time. My current understanding (which definitely differs from the documented state) is that there are two types of branches, local and remote branches, and both types of branches can be remote-tracking (it may not be possible to have a non-remote-tracking remote branch, though).

A local branch is one with a local branch head. In contrast, checking out a remote branch, while possible, leaves one with a detached head.

"remote-tracking" basically means that git-pull will update the branch according to changes in the remote repository.

Creating a branch using git-branch or git-checkout will always create a local branch which may or may not be remote-tracking according to the --no-track or --track options.

So there are basically three types of branches in a repository that I can see:

local branch, not remote-tracking local branch, remote-tracking remote branch, remote-tracking

The way to add a remote branch basically is not via git-branch or git-checkout -b (those always create local branches), but by editing .git/config.

Is this understanding correct or did I get things completely wrong? Because there is little sense in myself working on changing the documentation if I have not understood the situation.

Also, the documentation currently uses "remote-tracking" interchangeably for "local branch, remote-tracking" and "remote branch, remote-tracking", at some times claiming that one can locally switch to a "remote-tracking" branch, at other times not.

So the terminology seems fuzzy at the moment, and my attempt to clear it up might not be the preferred way of doing it.

Thanks,