Applied thought and sustained thought accompany entrance into the first jhana. It's useful to compare this to the simile of the bathman or the bathman's apprentice. Pouring the powder into the basin he periodically sprinkles it with water and meeds it into a solid mass.
The misconception I see here is that people read "accompanied by" and think it must be a negative thing. Surely, for it gets dropped in the later jhanas. It's not the case. You can't adequately approach entry into full absorption without some applied thought and some sustained thought.
"With the stilling of applied thought ..." - This occurs during the first jhana as the absorption is sustained. In other words "There is NO part of the body which he does not suffuse with the pleasure born of seclusion." In that case, applied thought comes to an end because of the first jhana, as a cause for the absorption - which in full/adequate/partial absorption takes out of being/existence/use.
Thereupon one switches gears and enters into and remains in the second jhana, pleasure born of composure, accompanied by joy and sustained thought. Like a pool supplied by a cool fount from within, having no inflows from east, west, south or north, with periodic showers from time to time, etc. etc.
The common denominator in the similes is the showering of water from above. Which implies the water is sustained thought. The bath powder is applied thought. One must "apply" thought to "sustain" thought. However, with the sustaining of thought one need not apply thought unless the purpose of going into jhana is not reached. So Buddhaghosa mentions we should hit and hit again at the object of meditation with our thought.
This is not "thinking" like "thinking about a girl" or "thinking about math". This is mental exertion from a proper perspective. If you were running away from a tiger through a thicket in the jungle, would you look back at the tiger as you ran or would you look ahead for branches and roots that might trip you up? How would you escape the tiger? The tiger is your impetus for overcoming branches and roots. Overcoming branches and roots means not falling in to the tiger's mouth.
Everything anyone needs to know has been said. Why is such a rich experience given one description and one simile a thousand times over? Because once you know it, those are the only words you will ever need to rely on. No more, no less. It couldn't have been any better put.