The distinction that really matters, at the counter, is not between GMT watches and watches without GMT: it's between GMTs that move the hour hand and those that move only the additional hand. These are two different mechanisms, with opposite usage philosophies.
The first type is called GMT traveller, or true GMT. The hour hand is disengageable from the train: it moves in one-hour increments without stopping the minutes. You arrive in Tokyo, push the crown, remove an hour. The local time changes, the GMT hand continues to rotate on your home time zone. The original Rolex GMT-Master I didn't work this way: its GMT hand was linked to the hour hand, so adjusting the time zone meant moving everything together. Convenient for reading two time zones in parallel, less convenient for those who change time zones while traveling.
The second type is called GMT office, or caller. The twenty-four-hour hand is independent from local time. You don't touch anything on the main movement: you only set the additional hand to the time zone you need to check. Local time stays fixed. This is the system used by the Seiko 4R34, the Sellita SW330-2, and many modern calibers designed for everyday work. It works perfectly for those who need to keep an eye on New York from a Milan office. It works less well for those who cross seven time zones in a week.
Reading the second time zone happens in different ways: central hand on a twenty-four-hour scale on the bezel, rotating disc under the dial as in the Miyota 9075, fixed bezel graduated as in the Tudor Black Bay Pro. The fixed bezel has a practical advantage that is often underestimated: it won't shift by mistake in your pocket or while sleeping.
Above simple GMT there are worldtimers, which must handle not only whole hours but also half-hour time zones, forty-five-minute time zones, and daylight saving time variations. The Bovet Récital 30 uses a system of rollers with dedicated pushers. The mechanical complexity of a serious worldtimer is an order of magnitude higher than that of a GMT caller.
A note on GPS Solar, which technically solves the problem at its root: the Seiko 5X83 caliber synchronizes via satellite and sets the time zone automatically. It's not a mechanical complication, but the result for the user is the same, with greater precision and zero manual intervention.