It’s been a while for me since I was in Mongolia, but I’m quite sure that, in this context, ‘jeep’ still refers to anything that resembles a Jeep.
When I was in Mongolia, the most popular ‘jeeps’, specifically for touring the country, were Russian made UAZ ‘jeeps’.
They tend to be quite similar to Jeeps. The kind I remember looked quite a bit like this.
“Jeep” originally referred to a small US Army scout vehicle built by Willys-Overland during WWII. More then 640,000 were produced and they were immensely popular with all Allied armies for their sturdiness, simplicity, and reliability.
Since then, “Jeep” has been simultaneously a brand name (of both military and commercial vehicles) that changed hands from Willys-Overland to Kaiser to American Motors to Chrysler and now Fiat, and a generic name for any small or medium-sized 4-wheel-drive on-/off-road vehicle, especially one with a soft top or a removable hard-top, regardless of make or country of origin.
This is more of english.SE question than a travel.SE one, but there you go. You can read the Wikipedia article here, but really nothing captures the spirit of the Jeep better than the famous Bill Mauldin cartoon.
Credit:stackoverflow.com‘