When should a pilot use the word "takeoff?"
The word "Takeoff" should only be used when clearing somebody for takeoff, acknowledging your takeoff clearance, or cancelling/acknowledging a cancelled takeoff clearance.

"Departure" should be used in all other circumstances, and as far as I'm aware whoever told you you could use the word Takeoff for VFR was wrong.

Anybody saying the word "takeoff" intends for an aircraft to enter, accelerate along, and then leave a runway in the immediate future: never anything else. Anybody saying otherwise should be immediately directed to the Wikipedia article for the Tenerife 747 disaster.