After reading Wikipedia articles on advection and convection, I still cannot determine whether there is a consensus on a difference between these two terms.
Sometimes, the term convection seems to include advection and diffusion, sometimes not. After all, equations exhibit two different terms for advection and diffusion, and we don't call the sum of them a convective term. When we talk about a convective term, it is indeed the advective term!
It seems:
transport of pollutants in a river by bulk water flow downstream relates to advection
boiling water for pasta relates to convection
Maybe, a conserved property such as energy can be advected, but we only use convection for transport of "ensembles of molecules".
So, is there a difference? Could we figure it out with examples?