Short-lived branches are likely referring to "bookmarks" in Mercurial. Or they could also just be un-named anonymous heads. These are different from what is exposed by the "hg branch" command.

Mercurial's "branch" was generally intended for long-lived things. Think the "stable branch" or a "version X" support branch for a project.

The branch name is baked into the commits that use it. You can hide them from the UI with "--close-branch", but they will still exist forever in the commit history. This is both a good thing and a bad thing, depending on your desires.

This is different from Git's "branch" which is basically just a pointer to a commit. It is not part of commit history, it is just a convenience for the developer. Later, Mercurial added "bookmarks" which are similar.