Usually the second miner also saw and included the same transactions so they are not lost. If they didn't the transaction is undone in a sense that it just didn

Usually the second miner also saw and included the same transactions so they are not lost. If they didn't the transaction is undone in a sense that it just didn't happen. Of course it can still be picked by the next miner. The chain that is longest (by difficulty) is by definition a log of everything that happened. Transactions that are not part of that chain are just candidates, nothing less nothing more.