The RSA and Diffie-Hellman protocols are part of asymmetric cryptography. But is there a word to distinguish between cryptosystem like RSA (i.e. there are two keys, one for encryption and another for decryption) and Diffie-Hellman (i.e. two parties have a public and private component that they share together to achieve shared key but finding private component will be useless if there is no one to share key with).
Essentially, I am trying to differentiate between key-exchange specific protocol vs. public-key cryptosystem.