What is a git topic branch? Does it differ from an ordinary branch in some way? Are there any branches that are not topic branches?
it looks like the most prominent and important type of branches that aren't topic branches would be release branches on a major, publicly-available repository, right?
That's probably right for you, but that's about you and the project you're thinking about; it's not determined by Git.
Most version control systems (particularly centralized ones) prescribe or enforce a particular workflow, including what it makes sense to use a branch for. Git ( and to some extent most distributed VCSs) consider that workflow, what branches are used for, when to commit, what different repos are used for, etc. is all chosen by the users and agreements among the users (policies). So Git doesn't enforce these technically.
This is one of the things that made Git hard for me to learn. Oliver Steele explained this from user's view, writing about Commit Policies.