After 14+ years wandering around the wild places of Wyoming and learning the land where horses call home, I tend to reference those places with half-names, nick-names, or as a general geographical location.
Other photographers also have their own way of identifying the places they wander with the wild horses, and sometimes those names are the same from one place to another, not necessarily because anyone intentionally named two places by the same name (this actually does happen in Wyoming on official maps), but because there are confusing levels of names for wild horse complexes, basins, and landscapes.
Sometimes even when chatting with others that live or visit here frequently there is confusion.... I can only imagine the confusion for those of you who are just trying to follow along with our shared images and experiences!

Link to WY HMA Map: https://www.blm.gov/sites/default/files/images/2024-10/WHB_HMA_2024_0.jpg
Wyoming is currently (per BLM) home to 14 Herd Management Areas [HMAs], at this moment there is an ongoing lawsuit challenging the planned zeroing out of the Great Divide Basin and Salt Wells Creek HMAs, and if we look at historical BLM maps there have been many (many) more HMAs across WY that have since been zeroed out and are now not even considered a Herd Area [HA] - that discussion is for another day!
Today I am focused on the name Red Desert - or as I often refer to it - 'the desert'.

Red Desert Complex HMAs
My first wild horse sighting in Wyoming was not in the Red Desert Complex [RDC], but the RDC is where I would learn the most about wild horses, in the beginning of my journey with wild horses it was the closest from where I lived then (Cheyenne), and with its fairly decent dirt roads most of the year, it was pretty dang easy for me to explore in the first couple of years when I was driving a 4-door Ford Taurus - not exactly the back roads adventuring vehicle!

RDC complex showing all five HMAs and the center HA of Arapaho Creek
In the beginning I knew nothing.... I am not really a naturally tech savvy person, I had a computer, but I had no idea what terms to use that would help me find more information, and the only BLM map specifically of the HMAs I could find was a tiny little thing that did not do more than give a general idea of where to find wild horses.
The desert is a strikingly big place, and I had no idea what was private, what was public, or that some of the horses wandering about were actually privately owned rather than BLM wild horses - all things that would take me time to sort out.
Slowly I began to meet more people that knew about wild horses, I met a couple of locals, and when we traded in that Ford Taurus for my first 4x4 rig - oh my - the adventures began in earnest!!
Those local folks showed me which 2-tracks to take and how to connect to other 2-tracks across the deserts open plains and high ridges - ohhhh the vistas I found!!!
I began to learn what was public vs private lands along with the history of the land and the humans that have called it theirs in the past and present. I highly recommend to anyone that regularly visits the range to download the onX Hunt app for your phone to keep track of land ownership - it is best to avoid trespassing whenever possible!
And in all that time, myself and those I was with, we just called it 'the desert' - the Red Desert, a land that to me is the place where the wild horses wander..... but is that correct - is this the only place called the 'Red Desert' where wild horses wander!?!
It is not.... there are in fact a few Red Deserts in Wyoming - in the same general area!
There is the town Red Desert found along a very lonely stretch of I-80 that has maybe two abandoned buildings and a dirt road that goes out into the Red Desert, we have actually travelled the dirt road that goes north from this tiny little dot on the map, a fun road, although I really recommend you have a 4x4 and lots of time to get lost and then unlost, if you decide to travel this road into the wild places.

Red Desert, WY
There is the Red Desert Basin, and as you can see it runs directly north from the town of Red Desert, if you were to take that dirt road out of town, after several miles, it takes you into wild horse territory.

And then there is the actual geographical Red Desert - an area that stretches across the place I call 'the desert' and then so much more.... I could not find a detailed map that clearly shows the lines of the actual Red Desert, there are a number of articles, books, and partial maps of the Red Desert as it is a place that many are passionate about both sharing and protecting.

Wyoming Outdoor Council Map - link to map info: https://reddesert.org/wp-content/uploads/2021/03/Red-Desert-Driving-Tour-Map-1-5.pdf
The geographical Red Desert area is incredibly massive, the above map shows it crossing the border into Colorado and a little corner of Utah, it stretches across from Rawlins to Rock Springs, it is on both the north and south side of I-80, Green Mountain and Crooks Mountain on the south side of Jeffrey City are considered a part of the Red Desert, along with various buttes and at least one or two other mountains (that I know of) belonging to a part of this vast place called the Red Desert.
And in that vastness are other wild horse lands.... which is what can be confusing, as some photographers refer to the Red Desert when sharing their images of wild horses from Salt Wells Creek, Great Divide Basin, Adobe Town, or White Mountain - none of which are a part of the Red Desert Complex - but all are wild horses of the Red Desert.

Wyoming Outdoor Council Map
So how can you know which Red Desert horses we are talking about!?!
Often I simply say 'Red Desert of Wyoming' and nothing else, because to me it is almost always about the Red Desert Complex wild horses, and because it is a complex where the horses have specific HMAs but also wander about across the miles, with only a few distinct herds not mingling together, to me they are really just a great big group of wild horses that can be found wandering in any part of their complex in any given season.
Some photographers use Red Desert in the much bigger sense of the vast high desert that encompasses millions of acres across south central Wyoming.... and it is also correct to say it in this way, and in some ways it is important to use the term, because we all need to understand how vast is this land that wild horses wander.

Salt Wells Creek HMA - February 2021
So in the end, there is no clear cut or concise answer of how to know, unless the photographer chooses to say in their post, or answer your inquiry for location - and sometimes us photographers like to keep a few secrets of our own. ;)
Hopefully now though you understand that when you see someone say Red Desert, it is not necessarily the same Red Desert where the gorgeous appaloosa stallion Looking Glass wanders... and it may not be the Red Desert that holds the horses of Salt Wells Creek, but no matter which part of the Red Desert it is, I can promise you it is a land of magic with awe inspiring vistas, it is a land that has always known wild horses and that the wild horses have always known as their land.