Clients don't confirm the transactions....
Transactions are confirmed when they're included in a block
I mean when the client shows "seen by x peers", are the peers not clients?
Sure, but confirmations are accomplished only by peers that happen to also be miners (or mining pools). There are no confirmations until a miner has included the transaction in a successfully solved and broadcast block that has been added to the blockchain. "seen by x peers" tells you nothing about the number of confirmations received (or does it mean there are 0 confirmations, I can't remember?).