When describing the function of a watch, I find the best way to start is with the situation. For a watch with the Caller GMT feature, you should think of a business executive who works with a company on the other side of the world. Or better yet, an American watch writer who works for an Australian publisher with a +14 hour time difference. As a writer, I need to know my deadlines by the time of my main office. Our main editor is there, so our articles and calls are scheduled on Australian time. To keep track of this, I will use Caller GMT. 
Caller GMT has a 24-hour hand that can be set independently of other hands. For example, the recently introduced Seiko 5 SKX Sport Style GMT is a Caller GMT. When you pull its crown to the first position, turning it clockwise allows you to set the GMT hand in hours on a 24-hour scale. Pull the crown to the second position, and you can set the time indicated by the central hour and minute hands. When you do this, the 24-hour hand will follow.
The function of the “real” GMT is different because the wearer’s needs have changed. Those seeking “true” GMT aren’t just worried about keeping track of time elsewhere. They are constantly on the move (hence the traveller) and need a watch that can easily keep up. Therefore, instead of having a different GMT hand, they had a unique hour hand. One of the most famous watches with this feature is the replica Rolex GMT Master. This watch was designed for pilots. Since pilots often travel between multiple time zones, they need a tool that shows the time at home.
At this point, you may be wondering why this type of feature is considered “real”. What is so unreal about the Caller GMT? The “real” designation is due to its early popularity with pilots. It is why the GMT function of the Rolex GMT Master is considered in many ways the purest and, therefore, the “most authentic” form of complication.
If you want to add a GMT to your collection, it is essential to keep in mind the GMT function of the watch. A “true” GMT is probably your best bet for those who travel a lot. If you tend to stay in a one-time zone but may have relatives in another country, a “caller” GMT will suit your needs. Just remember to research the calibre of the movement beforehand to see what it has to offer.
As for cost, there was a time when only a few companies offered “true” GMT functions. It meant higher retail prices. However, over time, more affordable options have emerged on the scene. The Hamilton Khaki Aviation Converter Auto GMT in the Time+Tide Shop is a great example. It, and many other watches, show that you don’t need to take advantage of the bank to enjoy this version of GMT functionality. All you have to do now is find an aesthetic that you like.