Is the nonce in Bitcoin the answer to the puzzle from the previous block?
Nonce of a header is the answer to that block.

Recall the mining process:


Create a template block header
Choose a nonce
Hash the block header
If the hash is lower than network difficulty, broadcast it. Else, choose a different nonce.


To sum up, nonces are for individual blocks, and a different nonce is chosen until the template becomes a valid block.