In a blockchain system, transactions usually form a {sender, recipient, amount} set which are signed by the private key of the sender to make sure the identity. However the exact implementation might vary depending on how the addresses are generated. In the easiest case, an address is simply the public key, consequently signing and verifying look as:
sign: data = sender, recipient, value with key = private key of the sender
verify: data = sender, recipient, value with key = sender (which is the public key of the sender)
However if more complicated cases, the public key of the sender is not stored directly, because the address is generated by an additional one way hash function of the public key. So at verifying the transaction, the public key of the sender has to be explicitly transferred or implied somehow:
sign: data = sender, recipient, value with key = private key of the sender
verify: data = sender, recipient, value with key = private key of the sender, which is however not the same as the address of the sender.
