Something that helped me keep everything straight in my mind is to compute everything in terms of power:
Radiant intensity: power / solid angle
Radiance: power / (solid angle and area)
Radiosity: power / area
When do we use radiant exitance over surfance radiance and vice versa?
To be clear, if how would radiant exitance and radiant incidence correspond? For example, if I had a perfect mirror, I would think that I would have M(x) = E(x). However, is it the case that M(x) = - E(x), so a mirror would have M(x) = E(x) = 0? Or is this not the case; in which case would a perfect mirror be indistinguishable from a light source?
Irradiance is the power per unit area entering a surface, while radiosity is the power per unit area leaving a surface, which does not depend on direction (this is the total power in all directions).