This thread has made me think of other ways jobs can be classified, but I don't play all of them so I'm shooting in the dark a bit here.

Mitigator - Job spends a good portion of time reducing damage to the party and themselves
Positional - Job has three or more skills that require rear or flank positions in order to optimize
Support - Job prioritizes based on current situation
Brute - Job brings damage. nothing else.
Pet - A modest portion of the job's kit belongs to the familiar they summon.

Also of note* There is no reason why a single job cannot go into multiple categories. Trying to assign a single category to FFXIV jobs is like trying to sort sporks.