Air Time: The time between when the aircraft leaves the surface of the earth until it comes into contact with the ground on landing.
Flight Time: From when the aircraft first moves under its own power for the purpose of take-off until it stops at the conclusion of the flight.
Airtime is thus the time the aircraft is aloft, while flight time is the "blocks to "blocks" as some people call it.
Airlines tend to use flight time because that's how long you will be sitting in the airplane for. It's also the one pilots log. It's not uncommon to see 1 hour air time with 1.5 flight time because of long taxi, waiting for other aircraft to takeoff or land, etc. Hence, airlines tell you the 1.5 hour flight time. That way, if they do it in 1.3 they look better!