I'm definitely no expert in here but, from posts I've read, I think you probably can have both.
It took my reading a lot of posts to understand the difference as I think the symptoms can be similar. I'd suggest searching on cuffitis and pouchitis in this forum to get a full understanding.
In very brief summary, my understanding is cuffitis is caused by remaining tissue with UC where the pouch is connected. Pouchitis is an inflammation within the pouch caused by bacteria in the pouch.