IIRC:
-- "goblins" is used in The Hobbit, but never in the LoTR. The goblins were living in the Misty Mountains, and didn't like the sun. They are the same as the small orcs from Moria in the LoTR.
-- there are little tracker orcs, like the one that was tracing Frodo and Sam in Morder on their way to Mt Doom.
-- there are the big orcs from Morder
-- there are Saruman's mutant big orcs
-- and probably more types shown, but this is what I remember right off.
Tolkein lets the origins of Orcs stay unclear; he mentions the theory they were created by Melkor from captured elves in the first age, but this is never stated as the definite origin anywhere I can recall (and I've read Hobbit, LoTR, Silmarillion, Lost Tales, and a bit more).
Tony