Asking him to drop his head and asking him to collect are actually two different cues using two different aids, but they're often used simultaneously.
To ask him to drop his head, you LIFT the reins, not PULL. Here's why:
When you PULL, you are exerting leverage pressure with a ratio of about 1:3 (depending on the length of the shanks, the balance, and the purchase). 1 pound of rein pressure = 3 pounds of pressure on the horse's mouth. The "purchase" is the part of the bit that attaches to it to the headstall. 1.) You pull the reins back, which activates the levers (shanks). 2.) The shanks cause the mouthpiece to rotate on its axis. 3.) Simultaneously, the rotation of the mouthpiece cause the purchase to pull down on the poll and causes the curb chain to squeeze the chin groove. 4.) The mouthpiece's port is pressed UP into the roof of the horse's mouth. The curb chain and the pull-down movements don't hurt the horse a bit, but what DOES hurt is that bump poking him in the roof of his mouth. So, he moves UP...away from the pressure that's causing him discomfort. The pressure is also in front of the girth line. Any pressure behind the girth is the gas pedal, any pressure in front of the girth line is the brakes. The bit activates pressure on the mouth. The mouth is in front of the girth line, so the PULL also makes him slow down because it can feel like a half-halt to him. A dull constant pulling back makes him back up (although if you ask him to back that way he'll always throw his head up...that's not how you do it, I'm just sayin'...) and if you do it hard enough, fast enough, and with long enough shanks, he may even go straight up on his back legs.
LIFTING the reins isn't the same as pulling. When you lift the reins, you're not actually exerting any force on the shanks. All you're doing is rotating the bit in the horse's mouth by moving your hand up and a little closer to the bridle. Instead of pulling back on the shanks, it just sort of picks them up a little, which rotates the bit on its axis just enough to rotate the port of the mouthpiece into an uncomfortable position in his mouth. When you LIFT, the port picks up a little off the tongue and rests against the roof of his mouth. He likes the port to rest against his tongue, so he repositions his head down, around the port in an attempt to put the port back in its nice comfy spot. We lift (or gently jiggle...or whatever you do to that affect) every time he picks his head back up. Eventually he learns that every time he picks his head up, that thing thumbs the roof of his mouth...it's not painful, just really annoying, so he leaves his head where it is...down. Oh....the difference between this rotation and the previous is that the curb chain is not activated. You can even see it from the ground if you stand by his head and just gently pick up a rein. The shanks move, but not enough to pull on the chain or the poll. That's why you need to leave a 2 finger space between the curb chain and the chin...because at this rate, the curb chain doesn't make contact with the chin groove until the shanks rotate the bit 45 degrees, which is kinda hard to do picking the reins straight up, but pretty easy to do when pulling back.
To collect the horse, you don't actually want him to pull his head back. What you really want to do is drive him up into the bit from behind, which is why you ask for a collection with your legs (by squeezing him up with your calves). Think of it that you're collecting him up from the rear. You're asking him to bring up the caboose to join the rest. Doing the lift and squeeze at the same time (or very quickly in succession) helps communicate to the horse that you're not asking him to go faster, you want his head down and his rear end not so strung out.