Either can be used to control either.
Its really not that complicated, but sadly this industry has a developed a compulsion to dumb things down to the extent that they can be rote learnt. Then people start getting dogmatic about it.
Personally, I'd rather take an energy based approach. If Thurst > Drag then KE + GPE is increasing. KE could be going up or down, GPE could be going up or down. But the sum of them is going up.
pb