Conquer Cycling Trainers are compatible with 26", 27" and 700c wheeled bikes. The trainer has its own skewer that replaces the one on your bike (making your bike, and many other bike models, able to work with it). The orange and white and fluid trainers will work with solid axle or quick-release rear wheels.
Regarding the trainer being compatible with either a gravel bike or a mountain bike, typically the thicker tread and wider tires associated with these may prevent the bike from sitting in the unit properly. If this is the case, thinner tires may be used and that should resolve any issues, as long as the bike fits the (above) requirements needed to use the trainer. There are many folks who prefer to swap out the rear wheel of their bike for riding on the trainer, as frequent "inside" riding wears the back tire more.
Regarding "fat tire" bikes, the resistance unit on Conquer trainers can accommodate tires that are less than 2.75 inches wide (the silver part of the resistance unit where the rear tire rests is 2.75" wide).