There are many kinds of vehicles that are considered off highway vehicles (OHVs). The term most often is used regarding dirt bikes, ATVs, ATCs, side-by-sides (Utility Task Vehicles or UTVs), dune buggies, and 4x4s but could also be used to describe snowmobiles and personal watercraft. Technically, mountain bikes and even off-road skateboards could be considered OHVs, but the term is usually applied to motor powered vehicles. You ride dirt bikes, ATVs, ATCs, Jetskis, and Snowmobiles, straddling a seat or saddle and using handlebars. You drive UTVs or side-by-sides, dune buggies, and 4x4s, sitting in a seat (with seat belts) and using a steering wheel. In most places you must be licensed driver at least 16 years of age to drive a UTV, dune buggie, or 4x4. Laws regarding dirt bikes and ATVs vary.
Dirt bikes are off-road motorcycles. They have two wheels. They are rated by engine size and typically range from 50cc to 650cc. Dirt bikes are the most difficult land based motorized OHVs to learn to ride. Like riding a bicycle, you must learn to balance the motorcycle to keep it upright but the engine provides a gyroscopic effect that gives some assistance. They are popular for riding single track trails and have the capability to ride on trails that cross slopes without falling over (unless the rider is careless or incompetent). An advanced form of dirt bike is the motocross bike. These are specially equipped and tuned for racing on motocross and Supercross tracks but you will often see them ridden by recreational riders on the trails. They are fast and powerful and capable of performing many stunts, such as wheelies and jumps in the hands of an experienced rider. Dirt bikes are usually designed to carry only one rider but some are or can be configured to carry an additional passenger with the addition of a second set of foot pegs and an extended seat.
Early motorcycles were, by necessity, off road machines, or, more correctly using today's language, dual sport machines. The lack of developed roads in the early 20th Century meant most vehicles had to be capable of at least some off road operation. The first dirt bikes specifically for off road riding and racing were custom made by riders themselves from Triumph and Rickman street motorcycle components starting in the 1940s. Then, seeing a potentially profitable market, Japanese companies like Honda, Yamaha, Suzuki, and Kawasaki started manufacturing factory dirt bikes for retail sale. A friend of mine bought the 2nd Yamaha IT 400 sold in the United States. Other prominent brands include KTM (Austria), Husqvarna (Sweden), and ATK (United States). Dirt bikes are made for riding in the the dirt. If you must ride on pavement, exercise extra caution. The knobby tires are not designed for use on pavement and could cause an accident. Dirt bikes are normally not legal to be ridden on paved roads but can sometimes be "dual sported" to qualify for occasional street use. There are special "D.O.T." knobbies that are street legal, but as with most compromises, they aren't as good on the street as normal highway tires nor as good in the dirt as off road tires. Ive read that most ATV accidents occur on paved roads and some of them have been fatal. Pavement isn't as forgiving as grass or dirt
Mountain bikes are sometimes considered off road vehicles and are banned from designated wilderness areas and many hiking trails. Properly equipped mountain bikes in the hands of a competent rider can handle remarkably difficult terrain. Forest and desert trails are popular venues for mountain biking. The "slick rock" area around Moab in south eastern Utah is one of the most famous places for mountain biking. Mountain bikes often share dirt bike trails in many locations.