How to choose the right bike? A ridiculous question for some, but for others it may be less so and for others it may help.
There are too many categories for a newcomer or a parent.
The basic category breakdown for mountain bikes is XC - AM - Trail - EN - DH - FR - Gravel - Fat bike. A simplified list of abbreviations can be described as follows.
XC, or Cross-Country, X country, XCO, XCM,....
XC is clearly performance oriented, for the Olympics, for marathons, for fast pedaling. The discipline where Jarda Kulhavy chases other racers for an hour and a half on TV screens during the Olympics or you go to New Town in Moravia to cheer for.
The model bike is very light, with a stroke of around 100mm, 29" wheels with finer tyres. Sometimes it has a telescopic seatpost.
Unsprung example is Pivot LES SL and full suspension example is Pivot Mach 4SL.


AM - Allmountain
Before we get into the specifications of the AM and Trail categories, please keep in mind that they are often confused and nowhere is it written that it is wrong either way. Respectively - Trail is perceived by some brands and people alike as AM and vice versa. So we recommend approaching the two categories a bit more openly and keeping in mind that not everyone may perceive it the same way. And it's nowhere in the bylaws:).
AM (allmountain) is an unreadable category for many, but it is, let's say, a more playful XC category. It's not so much about the travel, which in this category is around 120-130mm, but about the geometry that allows for comfortable all-day and multi-day rides while the bike has a big lean towards playfulness and downhill ability. By downhill, I don't mean time trial, but rather downhill for enjoyment without major limitations on the handling side of the bike. Semi-popularly written, you can ride such a bike quite solidly around a marathon (probably not for placing, but not for survival either), as well as a stage race or a day trip, go on the mission of your life, and have fun in local trails. It depends more on the skill of the rider, the bike has limits, so jumping a 2m drop into the roots on a flat with a bike like that is not a good idea.
The model bike is still relatively light. Strokes are somewhere around 120-130mm, 29" wheels are trending, it has a telescopic seatpost, a fatter front and a more rideable rear tire , more powerful brakes. Ironically the most optimal Pivot bike for this riding concept is called the Pivot Trail 429.

Trail
Trail - a category that many riders associate with AM, but is shifted a bit towards downhill characteristics. More robust construction, strokes around 130-150mm and geometry that is also fun to pedal, but the priority is the trail experience. Power pedalling uphill standing won't be as trouble-free as on the AM, but aggressive trail descents will be picked up more gracefully by the bike's construction. The "Trail" designation is a pretty clear indication of the type of riding the bike was primarily designed for.
The model bike has around 140mm of travel give or take, fatter and more durable tires on both wheels, more powerful brakes, and a telescoping seatpost. Most are fitted with air shocks, but spring shocks are occasionally found. Wheel dimensions are up to the rider. Both the prevailing 27.5" and 29" are standard.
A nice example is the Pivot Switchblade.

EN - Enduro
EN or enduro is actually a small downhill these days. The bike will allow you to ride to the top of a hill on the trails, but what an experience it won't be. It starts on the way down. The design of the bike is extremely durable and can handle everything from light forest trail, to alpine trails to some DH trails. You will often find that the bike's capabilities far exceed those of the rider :).
The model bike has almost downhill geometry, very durable tires and powerful brakes. Telescopic seatpost is standard. Shock absorbers are both air and spring. The standard wheel size is roughly half and half 29" and 27.5".
The top of the range enduro bike is the Pivot Firebird 29.

DH - Downhill, Downhill ( plus FR - Freeride)
DH means downhill. Downhill specials. Bikes with deep 180-210 strokes, a few gears and stable geometry just for going downhill. Uphill is done by cable car, car or on foot with the bike behind your neck.
The model bike has a double-crown fork, often a springy shock, specific geometry, a low seat, the toughest tires and brakes, and limited gearing. Wheels are 27.5", 29" and combinations - 29" in the front, 27.5" in the rear.
The super DH special is the Pivot Phoenix 29.

FR - Freeride is mostly based on DH bikes, but the suspension is set up for huge jumps and drops (dismounts), free pedals, downhill tires and high performance brakes. They're built for massive stresses on big jumps and riding down loose terrain.
Gravel
It's easy to think ofthe Gravel as a cyclocross bike. It's actually a road bike for broken roads, gravel roads and light forest trails. It has chunkier tyres, 700c diameter wheels (like the Favourite), disc brakes, often a single derailleur and a mountain cassette at the back. The Pivot Vault is an ideal example.

Fatbike
You'll recognizea fatbike ihed - massive tires. The original intention was to ride in the snow. Often the bike is unsprung and most of the whole bike visually revolves around the massive tires that don't dig into the snow as much. A prime example would be the Pivot Les Fat.

Downcountry
Downcountry - given the still-forming shape of the category, which has rather run out of "everything needs to be pigeonholed and named", we won't dramatise it just yet. A category that directs more fun into elite, or if you want a very performance oriented concept of riding. Thus, look for such bikes among XC specials, but with tuned geometry that dramatically saturates the riders' downhill trail experience. Feel free to use the PIVOT MACH 4SL for this.