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.
CY: I'd think that conduction is possible within gasses,b ut much less
so. Cause they would be more likely to convect.


ICBWB:
Convection seems to be limited to liquids and gases.
CY: Well, if you wanted to be a smartass, you could mention a
semiliquid like sand. But that's not really fair.


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.
CY: Sounds about right. Of course, radiation from the sun is supposed
to be a superhot ball of gas (plasma??)

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?
CY: yes, that would happen. Some air currents push hot air down.

Is this radiation?
CY: No.

Is it still convection?
CY: Pushing hot air down is still convection.

Or is it diffusion and for reasons of
definition, not one of the other three?
CY: Only three ways I know to transfer heat.