I believe that there are more than 2 general types.

There are service oriented submissives to genuinely enjoy doing things for their Dom, not needing or wanting to be forced into doing it, and their reward can be as simple as a smile or pat on the head.

Then there are the types that need to be forced into service and submission (and WANT to be forced) because they can't (or don't want to) give up that power without a struggle. I think it's a separate type of kink. "Bratty" subs may or may not fall into this category... thoughts on this would be appreciated. I'm not sure if I'd categorize "Bratty" separately or not.

There are bottoms, whom I feel are different than subs, in that they want to have things done to them (pain, forced service, etc) but on their terms and what THEY want... not so much what a Dom would NEED.

Of those three, I think there can be subcategories as well that would include subbies who are into humiliation, those who are into pain, etc. I don't know if I'd separate these 2 particular kinks from the others.