Cloud Bunny has it about right. In our airline we operate the A320, A321 and A330. Most of our Airbus pilots are 'mixed fleet' which means we fly all three variants. The A320 and A321 are considered a single type (same type rating), while the A330 is a different type.
A Cross-Crew Qualification course (CCQ) qualifies A320/1 pilots to fly the A330 and the two types may then be flown together using Mixed Fleet Flying (MFF) rules.
Some conditions include that we must maintain currency on both 'types' (1 landing every 35 days, 3 landings every 90 days) in both the A320/1 and A330. We are also not permitted to fly both the A320/1 and A330 in the same flight duty period (e.g. LGW-PMI-LGW on an A320 then immediately position an A330 LGW-MAN is not allowed).
But it's perfectly acceptable (and typical) to fly the A320 on Monday, A321 on Tuesday and the A330 on Wednesday.
CanadaKid raised a good point, despite being the same 'type' it is our A320/1 fleet which has the most differences (i.e. different engine types, avionics fits, weights etc... within the same 'fleet')!