backing up 12 seed words vs wallet.dat I installed electrum created my fist wallet and notice that instead of having to save a wallet.dat file, If I am right I just need to save/write  12 seed words.

If I understand properly the seeds used to create the wallet, will always produce the same output, but how does the recover process works in order to restore/recover the wallet balance?

Is the blockchain checked against my wallet keys to claim ownership of the transactions that where signed with my keys in order to recover the possible founds?
The seeds produce the addresses, not the balances.  Consider that you can have multiple wallets that contain the same address.  The balance doesn't exist in both addresses, because there's two copies ... it's like you said at the end.  

Your wallet looks up the addresses in the blockchain that's copied on your system, and they contain the balance ... well, actually, the balance isn't actually an entity.  The transactions are.  Your wallet scans the blockchain for your addresses, and any transactions that involved it, and calculates the balance based on the inputs and outputs.