Topic branches are typically lightweight branches that you create locally and that have a name that is meaningful for you. They are where you might do work for a bug fix or feature (they’re also called feature branches) that is expected to take some time to complete.
Another type of branch is the “remote branch” or “remote-tracking branch”. This type of branch follows the development of somebody else’s work and is stored in your own repository. You periodically update this branch (using git fetch) to track what is happening elsewhere. When you are ready to catch up with everybody else’s changes, you would use git pull to both fetch and merge.
I have also seen another kind of branch which is essentially a completely separate tree of files in the same repository. For example, the Git repository itself contains heads named man and html that contain entirely different content from the master branch. I don’t know what these types of branches are usually called.