There are various attempts at categorizing ADHD, of various levels of scientific credibility.
The one I hear most often are "predominantly inattentive" and "predominantly hyperactive".
There are also quack psychology tests that break it down into basically zodiac signs.
Such distinctions can have their uses for clearer diagnostic pictures or educating people who need to handle others' ADHDs, but they're not nearly as important as they are in diabetes. They're arbitrary and they don't completely change the mechanism of the condition, as far as we're aware. It just doesn't affect much.
In short, there aren't really formal distinctions because it wouldn't be very practically useful to have them, and because it would be hard to agree on universal types.
The location of this comma, really annoys me.