How can I tell the difference between display sleep vs. computer sleep on my MacBook Air (Late 2010)?
There's a really simple way to test this if you have another Mac, or any other machine really.

Turn on one of the Sharing features on the Mac in question (File Sharing, Remote Login etc.) and try to connect to it from something else. If the entire machine is asleep it won't work. If just the screen is asleep it will.

I assume you're connecting to some kind of wireless network with the MacBookAir, so you could also check the list of connected wireless clients on your router. If the entire machine is asleep it should not be connected. It may still show up in the list of DHCP clients (clients that have requested an address from the router recently), but it should not be connected.