The tab furthest to the right called "Addresses" where it says "These are your Bitcoin addresses for sending payments" I am using the Qt client. Reading that link now... thanks.
Those are addresses where you have spent Bitcoins in the past, e.g. you've send Mr. XY 2 Bitcoins, then his address will be listed there.
Exactly.
This is an address of someone (or some business) that you've sent bitcoins to in the past.
Don't I own my sending addresses?
No. The person (or business) that you sent bitcoins to at this address in the past owns the address.
Is there anyway I can get this BTC back?
If you contact the person (or business) that you sent the bitcoins to, they might be willing to send them back. If you look in the transaction history in Bitcoin-Qt, you should see when you sent bitcoins there and how much you sent. Perhaps that will help you remember where you sent them.