For Aaron: Aside from the 53 money transmission agent licenses both are required to hold, but only PayPal actually has.
Having a Bitcoin bank as a middleman is probably the best model for the majority of payments. But Bitcoin's appeal lies in its flexibility. Bitcoin is just a protocol: payments can go through a bank, but they don't have to.
One of the primary advantages of Bitcoin is its decentralization. I realize that Bitcoin != Coinbase and that Bitcoin provides a foundation for many potential services, but if everybody starts using Coinbase/<insert third-party name here> to handle their transactions, what's the difference? Where is the decentralization?
...Not that I think it's a bad thing if a bunch of Bitcoin transactions (especially microtransactions) go off the blockchain, I just wanted to point out that off-blockchain transactions weren't inherent to accepting Bitcoin through Coinbase.
So yes, there is actual bitcoin transaction going on if you don't have coinbase account.
However, you wouldn't want to, for example, run a gambling site that accepts and pays out bets immediately after they show up as 'unconfirmed' because you wouldn't have recourse if they managed to double spend.
You can't spend Bitcoin without the public knowing, and that goes for double spending as well.