In article , mm writes:
In high school physics, the three methods of heat dispersal were
presented as conduction, radiation, and convection?

Is that all there is? Is diffusion a fourth or is it subsumed by
convection?

Diffusion is conduction.

I could be wrong but:
Conduction seems to be limited to within a solid, or from the surface
of a solid to that part of a liquid or gas in contact with the solid.

No, conduction is present in liquids and gases as well, though it is
dominated by convection for significant temperature gradients (and in
the presence of gravity).

ICBWB:
Convection seems to be limited to liquids and gases.

That much is certainly true.

And ICBWB: radiation seems to be limited to from a solid or maybe a
liquid through a gas to another solid or maybe a liquid.

In principle radiation can be present within liquid or solid as well.
In practice, under normal circumstances, its range is so limited there
that it is indistinguishable from conduction.

As to convection, it was always described and seems to be limited to
broad currents, such as hot air rising and cold air sinking, but is
that all that happens? In, say, a room with moderate cooling in the
summer or moderate heating in the winter, while in general the hot air
rises, doesn't the random motion of some of the hot air cause it to go
downward and to mix with the cooler air below it? Is this radiation?
Is it still convection? Or is it diffusion and for reasons of
definition, not one of the other three?

Collective motion of masses of air is convection, random motion of
individual molecules is conduction.

Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"