Each private key corresponds to one public key. That public key can expressed in two ways - compressed and uncompressed - but they both refer to the same point on the curve. There are almost 2²⁵⁶ possible private keys, and the same number of possible public keys (or double that if you count compressed and uncompressed public keys separately).

There are only 2¹⁶⁰ possible P2PKH addresses though, since to reach an address you must use the RIPEMD-160 function, which outputs a 160 bit result. So there are in the region 2⁹⁶ possible different private keys which will all give the same address (and again, more than that if you consider compressed and uncompressed public keys separately).