If I'm using both a digital certificate and a digital signature in a communication:
Are there four different keys in operation here, since key pairs are mathematically linked? Is the Digital Certificate using one set of keys, i.e., a private key to encrypt the hash and a public key (on other side of conversation) to decrypt the hash (so at the other end the hashing algorithm can be run to determine if data has been altered), and an entirely different pair of keys registered with the Certificate Authority in order to verify you are who you say you are to the person you're sending to? Or is that same exact public key/private key being used in both scenarios?
I'm sure this question is indicative of a lack of proper understanding of process, but I don't see it spelled out anywhere and am unable to implicitly understand based on the numerous explanations I've read.