Public address cf private keys cf blockchain sigs

[davidpbrown]

If a transaction is signed by two different private keys related to the same public address, is the signature different?
I'm expecting perhaps not, since I'm wondering that it must be the public key that contributes to the confirmation that a signature was actioned by an 'pwner' of that public address.

If there's a simple description of how a public address is used to confirm a signature that was actioned by a private key, that would be interesting to see. I don't understand yet how the private key actions a signature but the public key cannot.