Greetings. I was wondering if anyone knew of such a solution which allowed you to accept PayPal payments, and send money in a "PayPal Format" without actually having a PayPal account per-say. Does something like this even exist?

Thanks in advanced :).

If you don't have a paypal account, you cant send/accept money through paypal.

If you don't have a paypal account, you cant send/accept money through paypal.
Take a look again over my post :). That's part of my question! Does something exist that allows you to send/receive PayPal payment's without actually having a PayPal account?

no - nothing like this exists

you have to have a paypal account to receive money. I do not think you have to have a paypal to send money (given you invoice them)
You will need a merchant account and gateway like authorize.net to do what you need in case you were not aware :)
If you are looking to be a webhost, this would make you look more professional.