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!
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?