The difference between "popping" and "dropping" in my reading is that some planes have the flare ejection system aimed upwards, which primarily helps with threats from behind as the flares fly up as they "pop", then drop into the trail of the aircraft, while some systems are aimed downwards and also mostly to the side, so the "drop" flares which are better if the expected threat is going to be below the aircraft.
This is just conjecture from me, it might be BS, but I see most fighter jets have flare systems aimed upwards, while some transport planes and helicopters have it on the sides on the low side. In case of the helicopters, it might also be there to avoid getting in the rotors. I'm no military pilot, though, so take this with a mine worth of salt.