Aiport Extreme & wireless router simultaneous?

Sorry if this is a stupid question but am a bit confused with the following...

My internet router is connected by ethernet cable to an Airport Extreme basestation. From my MacBook Pro I can select the Apple network that the AE provides using the Airport dropdown. I can then use the internet and my external hard disk (connected to the AE) with no problems.

The internet router is also wireless and I can see this network in the Airport menu. If I select this then I can use the internet but I can also still use the external hard disk connected to the AE. Using the router admin tool I can see that the AE and laptop are both connected to the router separately.

I am a bit confused here...surely I can only connect to either the Airport Extreme or the wireless router using Airport?

Technically no. It's just like having more than one ethernet card in your computer. Each one can have a different ip address and be accessing a different router if you had 2 different modems to connect to. In your case, one is hardwired, the other is wireless. If you look at the ip address for your wired and wirelss, you will see they have different ip addresses.

Every device connected to the router will be connected separately. How would it know where to send data if two devices had the same address?

Sounds like you have set it up similar to my setup. The router handles all DHCP on the network. The AE is in bridge mode and receives it's IP address from the router. Therefore, it is on the same network as the router.

I then have two wifi networks, one on my router and a 2nd on my Time Capsule (same as AE). Although, mine are separated by 100' and are located at opposite ends of the house. That way, I can connect to whichever wifi is providing the best signal, depending on where in the house I am located. If your router and AE are sitting side by side, there's probably not a whole lot of point in having 2 wifi networks set up.

And yes, you can only connect to one of the wifi networks at a time.