Nonce
A number used once; in mining it is the value that is changed while guessing, and in accounts it counts a sender's transactions.
In proof of work the nonce is a field in the block header that miners increment as they search for a hash below the target, and because that field is small they also vary other parts of the header to extend the search space. In account-based chains the nonce is a per-account counter that increases with each transaction the account sends, which forces transactions to execute in order and makes an old signed transaction impossible to replay. The account nonce is also what causes a stuck transaction to block everything behind it, since a later nonce cannot execute until the earlier one is included or replaced. The two meanings share a name and a general idea of single use, but are otherwise unrelated mechanisms.
In practice
Replacing a pending Ethereum transaction means broadcasting a new one with the same nonce and a higher fee, so only one of the two can ever be included.
The common misunderstanding
The mining nonce and the account nonce are different things: one is a search value in a hash puzzle, the other is a counter that prevents replay and fixes ordering.