BA's A321s seat 188 max, the A320 seats about 160. A321 is a stretched version of the A320, being about 7 metres longer than the A321.
A321/A320/A319/A318 are all part of the Airbus A320 'family'. As such, crew have common qualification for these types, and they share components. This means that BA's LHR flight crew are qualified on the entire Airbus shorthaul fleet and it also means maintenance costs are reduced. I think it's similar for the A330/340.