Air mode allows the props to spin at a predetermined RPM ( can set in Beta Flight ) when at 0 throttle thus eliminating dead props during high speed maneuvers.
I have mine set to a function sw on the Taranis, so once armed I can switch on air mode when I want it.
Idle up differs in that it is controlled by a switch. When you normally go to zero throttle, PIDs are disabled but with idle up activated, you still have all stick control. That is how Steele and others do those cool slo-mo floaty inverted manoeuvres