The miner with the most blocks or the most proof of work will be the acceptable block and the once with shorter blocks or that were generated will less difficulty will be dropped.
A stale block is a block that was confirmed but has now been put back into the mempool.
Because a block might be in the blockchain that might be dropped, so the 10 minute block time decreases the chances of stale block and so waiting for more confirmations limits the prabability of your transaction being in a stale block