They do. A330/A340/A350 are all on the same type rating. A319/320/321 are on the other Airbus type rating. Boeing has the 737, 747, 757/767 and 777/787 types. Boeing has more type ratings because there is less computerization, all airbus planes fly the same under normal law.
Well, that was weird. A quick Google search doesn't answer it directly but it might be something like:
FAA (and maybe EASA) takes it as 2 types but it only requires a difference training from the 330->350.
From the link: The new regulatory approval means that pilots who are qualified and current on the A330 can already commence their preparations to take the A350 XWB’s controls by undergoing “differences training” only
