It's not quite as simple as you suggest but, in broad terms, you are correct. For example, a pilot who has completed a type rating course on a B757, although his licence will show B757/767, cannot fly a B767 without further approved training (differences training). On the other hand, the A320 type rating includes A318-A321 as a single variant and so a pilot who has completed a type rating training course on, say, the A318 can fly any of the others without further training. The A330 and A340 are separate type ratings, although there is provision for abridged training from one to another, so-called Cross Cockpit Qualification (CCQ).
The list of type ratings and variants is on the EASA website for both
Aeroplanes and
Helicopters