I don't know specifically in mapping, but in lighting terms they refer to falloff.
Inverse linear is exactly what it says on the tin - a linear gradient where the light will fall from full intensity to 0 over a distance or percentage specified.
Inverse Square refers to how light actually behaves in reality, and can be calculated thusly:
Illumination = Luminosity divided by Distance squared.
In plain English: An object twice the distance from the light source will receive only a quarter of the illumination of the source.