Nope! 'Squeeze', 'press', 'slap', or, 'pull' the trigger DO NOT mean the same thing; nor can these terms be (correctly) used interchangeably between either: (1) specific (and prerequisite) methods of firing a weapon, or (2) interchangeably among rifles, pistols, and shotguns.
The general consensus (with which I agree) is that you, 'squeeze' a rifle trigger; but, 'press' (or, 'slap') a combat pistol trigger. 'Pull' is an archaic term that is being less and less frequently used nowadays.
Me, personally? I, 'press' (or, 'slap') pistol triggers when I'm firing quickly and at close range. Different pistols, however, have different lockworks; and certain pistols cannot be fired from the reset position: e.g.; my S&W Model 41 in comparison to my Glock Model 21. I'm forced top, 'slap' the trigger on the Model 41 in order to make it repeat rapidly; but, on any model Glock pistol I'm able to repeatedly, 'press' the shots off from the trigger's, 'reset point'. *
The ONLY TIME you want to, 'squeeze' a handgun trigger is when you are firing precisely, and usually at targets farther than 15 yards away. (I do, 'squeeze' pistol triggers; BUT always at targets farther away than 15 yards.)
While trap shooting I tend to, 'press' (or, 'slap') a shotgun trigger as I follow a moving target. I defy anyone to, 'press' (or, 'slap') a rifle trigger while firing at long range targets, AND hit the target. THAT, ain't never going to happen! **
Whether you should, 'press', 'squeeze', or, 'slap' a trigger depends on BOTH the weapon, and the trigger mechanism, as well as what you're trying to do with that gun and a specific target.
As for your final question about, 'What' YOU should do with your pistol trigger at the range? My friend, WATCH YOUR FRONT SIGHT, AND LET YOUR TRIGGER TECHNIQUE TAKE CARE OF ITSELF! The three, 'classic elements' you should be focused on are (1) Your grip. It should be highly consistent and always the same. (2) The trigger. Use the correct trigger technique for both the weapon, AND what you're trying to do; and (3) your front sight. If you don't watch it (and the target in the background) very carefully, then all sorts of shooting errors and missed shots are going to creep in on you.
* The term, 'slap' implies that there is some distance (or daylight showing) between the trigger's face, and the pad of the shooter's trigger finger. If that space isn't there, then the term, 'press' is more applicable.
** Perhaps I, 'slap' my shotgun triggers because all of my shotguns have been either of Browning manufacture, or pump action.