No. Just like shaggy404 said above, this is your change. The second amount is still on your control.
I don't think there is any wallet that charges fees for transactions. And If any of them do, you shouldn't be using them in the first place.
When the output of a transaction is used as the input of another transaction, it must be spent in its entirety. Sometimes the coin value of the output is higher than what the user wishes to pay. In this case, the client generates a new Bitcoin address, and sends the difference back to this address. This is known as change.
You should read this:
https://en.bitcoin.it/wiki/Change