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. 
A: Convection and conduction are essentially two different macroscopic approaches to deal with what is fundamentally the same phenomenon on a smaller scale.  Convection is basically just Advection and conduction packaged together for simplified analysis. 
You mention that it's not "mutually exclusive, collectively exhaustive" (MECE); but if I understand the concept correctly, the analysis normally is.  
Convection and conduction may behave the same on a fundamental level, but the methods we use to analyze convection and conduction are not the same.  You might be able to argue that the convection analysis is really just a series of conduction analyses; but when used in the context of heat transfer equations, they are generally treated as part of a "mutually exclusive, collectively exhaustive" system.
If you only apply the conduction analysis to solids, and only apply convection when there are fluids (and also account for any other mode of heat transfer, such as radiation), you can develop a system that analyzes conduction and convection completely separately (mutually exclusive), but is able to determine all the heat transfer occurring (collectively exhaustive).  
There will be situations where fluids will have no movement; and thus analyzing convection is functionally equivalent to just calculating conduction.  As long as you only and always apply convection analysis where there is potential for fluid flow, and only and always apply conduction analysis where there is no potential for fluid flow, you will be able to incorporate both heat transfer modes at the same time into a "MECE" analysis; even though they are based on the same underlying process.
