Mountain bikes are built very differently from hybrid and road bikes. Mountain bikes are visibly different from other bikes. Mountain bikes differ because they generally have:
Fat, knobby tires. What is meant by fat tires refers to both their width and height. Mountain bike tires are very wide so they can get a lot of grip on the trail. They are tall so they can more effectively abosrb large jolts without damaging the rims. They are knobby so they will be able to better grip the terrain. The main focus of mountain bike tires is grip. This is necessary for steep uphills. In some situations a skinny smooth tire would spin on the trail, and that is why knobs or aggressive tread is necessary.
Thicker frames. Mountain bikes generally have thicker frames than a roadbike.
Monster suspension. The largest difference between hybrid bikes and mountain bikes is their suspension. Mountain bikes have large suspension travels compared to hybrid bikes. When you press down hard on a mountain bikes' handlebars you will feel the bike's fork compress. This is its front suspension. Some bikes called soft tails have suspension also in the rear. This is a component mostly unique to mountain bikes. But what is suspension? Suspension is what allows the wheels to 'travel' up and down. This lets the bike absorb jolts to make your ride smoother. The more 'travel' the more comfortable your ride will be.
Shifters. Mountain bikes have a style of shifters that I have not seen on any other type of bike. They are best described as 'paddle shifters.' Paddle shifters have two paddles on each handlebar. To shift up in the rear you pull on the smaller paddle in your left hand, to shift down you push the large paddle on the same handlebar. You can push the large paddle in more and be able to shift two or three gears at once! A bike with 'twist shifters' is not a mountain bike. Twist shifters are awkward to use. It can be accidentally shifted, and creates difficulty shifting when standing and using your handlebars to add torque to your pedal strokes. Even beginner mountain bikers should have a real mountain bike.
You will be able to find whatever you need from a local bike store. You can use Google to find one.