MacOS – Swiping trackpad no longer wakes Macbook Pro from sleep in OS X Lion

There are really three, sort of, but they're not exactly as you described:

1. Display sleep: The screen goes blank after a certain amount of time. You can wake up the screen by touching the trackpad or pressing a key.
2. Sleep: In this state, the computer goes to sleep: the hard drive stops spinning and the CPU uses much less (almost no) power. This can be invoked by closing the lid of the laptop, selecting Sleep from the Apple menu, or via a timer. You wake up the computer by opening the lid or pressing a key.
3. Hibernation: If the battery is almost dead, the laptop will hibernate to save power. This is similar to shutting down, except all the contents of RAM are dumped to the hard drive, which makes it much faster to start up (as well as starting the computer up into the previous state). You have to hit the laptop power key to wake the machine from hibernation.

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.