There are many breeds. Just to make a few, American Shorthair, British Shorthair, Maine Coon, Canadian Sphynx, Abyssinian, Siamese, Scottish Fold, Devon Rex, Persian, Birman, Ragdoll, Norwegian Forest Cat, Bengal, an my personal favorite, whichever cat is closest to me at this time.
Compared to dogs, sure, it's barely a fourth that number. There are not "very few cat breeds and just a lot t of coat patterns", though, I wouldn't say that anyway.