[derekm]

What is the difference between and usage of
runTime.timeName() versus mesh.time().timeName()

Specifically in the use of IOobject.

I'm in the process of trying to create a new new absorption emission sub-model, that is constant with respect to time but varies with its location in the mesh.

[floquation]

Nothing.

runTime is a variable declared in your solver that refers to the Foam::Time object.
<-- Useful in your solver

mesh.time() retrieves the same Foam::Time object, as the mesh has access to Foam::Time.
<-- Useful everywhere else, where the variable 'runTime' is not accessible.