The rear hub for road bikes is designed around a 130mm OLD (over locknut dimension). Mountain bikes are designed around 135mm. That means that a mountain bike wheel doesn't have to be dished quite so much and is consequently stronger. It also means that an unmodified mountain bike hub won't fit easily onto a road bike.
Many mountain bike front hubs have larger diameter axles.
Mountain bike gearing is much lower than road bike gearing.
At the present time, the upper end road bikes use 10-speed rear cassettes. Mountain bike cassettes have only 9-cogs. This makes it possible for mountain bikes to use a wider chain which some riders claim is stronger and/or longer wearing.
Shimano mountain bike rear derailleurs are offered in "Rapid Rise" (low normal) design. this causes them to shift opposite from road bike derailleurs. Some riders find the rapid rise design works better in certain hilly conditions.
All road bike front derailleurs are actuated by a cable that pulls from beneath the bottom bracket. While down pull mountain bike derailleurs are available, most mountain bikes frames are designed for top pull front derailleurs. Mountain bike front derailleurs are also offered in a top swing design in which the derailleur cage is located above the parallogram mechanism.