[artmageddon]

VBprogrammer's post is pretty spot on.

In my experience around towered airports, I can't say I've heard "take-off" used in any radio comms I've had. In the example you've given, "departure" would be used instead of take-off as you've said. Towers are encouraged to use other terms[0], like the following:

"N1234 cleared onto the active runway" which means you're free to proceed with your take-off roll.

When you leave the airspace(at least at a class D airport), the controller will contact you with "N1234 frequency change approved", which means you either contact the next frequency planned in flight(such as flight following, or no frequency if you're just flying around in class E).

[0] http://www.faa.gov/air_traffic/publications/atpubs/atc/atc04...