Yes sky330, it depends.
You can have different variants on the same type certificate, but you can also have seperate type certificates for customized variants.
For example the Dornier Do27 (single piston engine light aircraft), the Do 28, Do 128 up to the Do 228 (twin engine turboprop commuter) have the same type certificate.
On the other hand the Boeing 747-430 (Lufthansa) and 747-428 (Air France) do not have the same type certificate, although they are almost identical. To be true, the 747-428 is not type certified in Germany, as well as the 747-430 is not type certified in France.
(The 747-400 is pre JAA type certified, so there were national certifications)
So the rules are the same for most authorities, but the politics of the manufacturers is different. (you can make LOTS of money ´designing´ and approving the same type of repair for every operator, say for every type again ...)