Signatures are dependent on the data they are signing and my public key, my public key is fixed but the data I am signing is not. I can add and remove transactions to the block to change the output of the signature. (Technically with ECDSA signatures you don't even need to do that, you just change the nonce used in signing to get a different signature)
The generation signature only depends on the previous block generation signature and your public account number. Nothing more.
Part of the generation signature (called hit) is used to determine a queue of forgers. First in this queue is allowed to forge. If he did not, it is the turn of the second in the queue and so on.