A miner hashes the block header which consists of nonce, time, previous block hash, and merkle root.
While it is probable that the time, and prior block are the same and each miner will attempt every value in the nonce range the merkle root will always* be different. The merkle root contains all transactions including the coinbase (which has pool or solo miner reward address) and thus will be unique to the pool.
*Although in cryptography technically nothing is possible the probability that two different sources of data will produce the same 2^256 bit hash is so highly improbable that it can be considered impossible for all intents and purposes.
A more likely scenario is an improperly configured pool sends the same block header to two miners. If they get credit depends on the pools stale share detection algorithms. Still even if they get "credit" that is bad because the pool is duplicating work. If pool did this enough (say 10% of the time) this would be noticeable in the pool's "luck" since pool is only doing 90% actual work (and 10% worthless duplicaiton).