Q:

Is convection just a variant of conduction where the matter is circulating?

I.e., are the following statements correct:
Conduction - Your body loses heat through direct contact with solid matter
Convection - Your body loses heat through direct contact with circulating liquid or gaseous matter. This is actually a variant of conduction. Air or gas next to you is warmed by conduction, but then that air or gas moves away (since it's circulating), and is replaced by colder air or gas that gets warmed again, and so on.

A:

You are correct. Ultimately all heat must be transferred from one molecule to another via collisions. That's conduction. But it makes practical sense to distinguish between conduction and convection because their rates are very different. Place two hot eggs into two cold buckets. Stir the one, leave the other one unstirred. Which egg cools down faster? The one that's stirred. That's of course because stirring brings cooler fluid close to the hot egg, which helps remove heat faster. The mathematical equations that describe each case are different, hence we study conduction and convection separately. 

