I used to sell snow blowers and the run down is:
1. Single stage snow blowers are light duty electric, battery, or gas machines rated for up to 6". 6" of powder. Heavy wet snow will be more difficult and the depth it can handle reduces. Most importantly they are meant for hard surfaces only like concrete or asphalt. This is due to many components being plastic or not strong enough to handle the stress of uneven surfaces like gravel or picking up loose debris that can cause damage.
2. 2 stage blowers are almost always gas and offer more power and the ability to move more snow per hour and throw it farther. They can be used on any surface including gravel and are made of stamped or welded steel with more robust components. Quality depends on manufacturer and price point.
3. 3 stage blowers have and extra auger that channels and moves snow even more efficiently. These can move deep snows and are meant for large open areas.
So in short, the surface of your run is the main consideration. Using a single stage blower on gravel, mulch or other soft surface will result in clogging, damage, or ultimate failure in the machine. This can occur on the first use or after repeated use, but odds are very high for issues.