Regor,
As the Airbus A319/320/321 share a common cockpit concept, you will find that most conversion courses will rate you for all three types. Naturally, there are differences in terms of MTOW and MLW and they may be fitted with either IAE V2500 engines or CFM-56. Some companys operate only one engine type, other may want familiarity with both. At the airline where I instruct, we deliver a course covering all types, in addition to which, there is a short "differences" module to cover the fuel system on the A321
Hope that helps,
Blue skies!