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Darren,
The list of variations is almost endless! There are even designs that not many people have heard of like the 'Kletsov' (which Bert uses), Dall-Kirkham, Gregorian, Shmidt-Vaisala, Argunov, etc etc.
But there are basic ones that are more common: Schmidt-Cassegrain, Schmidt-Newtonian, Maksutov, which all use a very similiar optical system with variations in mirror shape, and corrector plates.
Refractors have mainly 3 configurations: Achromat, ED/Semi Apochromat, and Apochromat. Each having better quality lenses progressively.
and the list goes on.
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