It may sound like verbage, but I believe it is real, as each gives a subliminal message to the brain, I prefer press over any other word. The technique is valid on everything but a release trigger. As Rob teaches, extend, touch, press.
The difference ( to me ) is take the word squeeze, its like milking a cow, the WHOLE hand squeezes, We don't want that, we only want our trigger finger to be busy, not the hand muscles.
Now pull, equals in my mind, Jerk the trigger. You can pull a boat, pull a fast one, pull certain body parts, but don't pull your trigger.
The press, is pressing the trigger straight back, regardless of the action, SA, or DA, and mindless of weight, if it is time to press, then we press, hard or soft as the firearm dictates. It is a method, and a lot of top shooters and trainers use it, because it works for all firearms. When I shoot precision firearms, and the AR15, I do not use the cheek weld, shooting thumb over the grip, and weld my cheek to my thumb, I allow my thumb to ride along side, the right side of the firearm, with this application, I cannot squeeze the grip as I press the trigger, I am right handed.
Release trigger, usually only found in shot guns, for competitive use, you press the trigger, and it fires when you let go, no possibility of a jerk, theoretically.