Dirt and motocross bikes are very similar to each other. They are both built to be used on all terrain race tracks that may be made of mud, dirt and similar substances. A person can often spot a dirt bike by looking at it closely. It will have a much beefier body than its motocross counterpart. Dirt bikes are bigger in terms of both appearance and performance. They will be heavier and able to handle higher quantities of fuel.
Motocross bikes are made for a very specific controlled racing environment. Due to this their design is more concerned with power than safety issues. In the world of motocross the track can be adapted to make the bike safer, not the other way around.
In contrast dirt bikes are made for more natural trails that can not be adjusted. Therefore the bike itself needs to be able to change depending on the conditions of the course. Dirt bikes tend to have lower maximum speeds due to their high pick ups. However, the suspension of these bikes is far more powerful. They also tend to have headlights built in for driving in the dark. Motocross bikes do not generally need these lights as the race will likely be held indoors with artificial lighting instead.
Since dirt bikes ride in natural environments they have more shielding on them. The main areas to protect are the engine, as well as the hands of the rider. “Bark busters” are ideal in this regard. They prevent damage caused by tree bark and other large debris. A motocross bike will be visibly lacking in shielding.
Motocross bikes are built for sharper turns whereas dirt bikes are more about endurance. Because of this, a motocross bike will have much narrower gear ratios. A dirt bike will often go long stretches without the need for changing gear, so their design is not such an issue.
The exhausts are also built differently. Even though dirt bikes are only intended for races they may still cross roads on occasion. Therefore they need to conform to road standards. This apples to the level of noise that they make. These levels are reduced through engineering.
Motocross bikes do not face this issue. Their engines are known for their loud power. In fact this is part of their wide appeal. They tend to not have any mufflers or other silencing devices.