What are the types of pugs?

Well I'm guessing by type you mean colors, so the only real pug colors accepted by the akc is fawn, which is a tan color with a black mask and black ears, there is also a black pug. As far as others there are brindle and white, which are not accepted by the AKC and no responsible breeder would purposely breed these colors. They maybe cute and they may even be called "rare" they are not really true to the breed, and would never be allowed in dogs shows.