What are the 3 main classifications of meteors?

The three main types of meteorites:
1. 'The irons' come from the core of an asteroid or planetoid and are heavy and large.
2. 'The stoney types' come from the crust of a planet or an asteroid. Most times they contain little round grains called chondrules, these grains are nearly as old as the solar system itself.
3. 'The stoney-irons' come from a region between the core and the mantle layer of an asteroid or an early planet, this type of meteorite is rare. As far as I know there aren't any 'specific' names for the three types of meteorites (I assume you mean that as there aren't any specified classifications of meteors). I do hope this helped.