Had answered it long back on RG, for a similar question ... Copying the same answer here ...
They are synonymous in absence of molecular diffusion but if diffusion is present the case changes.
For advection the property distribution is same (eg: a thick paste like thick glue in water, the drop moves in water but it doesn't mix easily) when the fluid element is transported but when diffusion is present the property distribution is flattened and is spread out (eg an ink drop in water, ink diffuses and the dense color slowly re-distributes in the surrounding quiescent fluid). In convection generally the bulk transport is present as a combination of both advection and diffusion.
Convection is the movement of a fluid, typically in response to heat. Advection is the movement of some material dissolved or suspended in the fluid. So if you have pure water and you heat it you will get convection of the water. You can't have advection because there is nothing dissolved or suspended in the fluid to advect. If you have silt suspended in the water and heat it then you will get convection of the water and advection of the silt.
Convection always transfers heat in the vertical plane while Advection heat transfer differs from convection in that the movement of heat is confined to the horizontal plane.
Heat transfer by convection is due to two effects;
1- Heat transfer due to molecules collision and vibration as a result from temperature change and it is named CONDUCTION, and
2- Heat transfer due to bulk motion of molecules (Free motion due to density difference or Forced motion due to pressure difference); this named is advection
Heat by convection = Heat by CONDUCTION + Heat due to fluid motion
Convection is the movement of a fluid, typically in response to heat. Advection is the movement of some material dissolved or suspended in the fluid. So if you have pure water and you heat it you will get convection of the water.
Thermal diffusion added to transportation of thermal energy by inertial of fluid flow(known as advection), is generally known as CONVECTION. Convection is not a fundamental mode of heat transfer. If temperature of the body and fluid is same, heat transfer is never possible by fluid inertia (or advection.