Can a digital signature scheme also be an encryption scheme? Using Schnorr signatures, one could devise a system where a single public key can represent multiple signers. Do signature schemes like that represent crypto systems usable for encryption? 

In that case, could you say that a signature scheme and an encryption scheme represent the same thing?
In that case, could you say that a signature scheme and an encryption scheme represent the same thing?


I don't see how.  With a signature scheme, the public operation can return just a single bit (either "the signature verified" or "it didn't").  It's not at all clear how you could efficiently use a function that returns a single bit as a part of an encryption operation.

Now, there are certainly cryptographical primitives - such as modular exponentiation within RSA - that can be used as a primitive within either a public key encryption or a signature scheme; however there are also signature schemes that cannot be used to do encryption, and so generically, the two classes of schemes cannot be identical.