You're thinking of "somewhat homomorphic encryption", which is homomorphic encryption that can support both addition/OR and multiplication/AND, but only in circ

You're thinking of "somewhat homomorphic encryption", which is homomorphic encryption that can support both addition/OR and multiplication/AND, but only in circuits of a limited depth. The original FHE paper did indeed prove that you can rework any "somewhat homomorphic" system into a fully homomorphic one. Partially homomorphic encryption is different because it really only enables one of those two types of operations. For example, Pallier encryption has the property that Enc(A) + Enc(B) = Enc(A+B), but there's no way to go from Enc(A) and Enc(B) to Enc(A×B).