I have used it the same way for everything I have flown in game: Warthog, Su-25T, F-15C
I imagine its exactly the same for all the others.
Thrust up increases the throttle in increments based on how many times you push it.
Power up is used to adjust the throttle by holding it down, and will gradually go up/down.
Power up/down is nice when every second doesn't count and you get to set the exact amount of throttle you want based on how long you hold it.
"THRUST UP" is nice in a tight spot, 68% throttle in F-15C? Hit that button 4 or 5x rapidly and in less then a second you just set your throttle to 115%.
I am unable to check in-game...but the preset thrust up/down for the F-15C is like 75%?, 83%, 99%, 105%? and 115%