Global Illumination: any lighting that involves more than just the surface being shaded. The strict interpolation already counts shadows as a global illumination effect, since that requires the interaction of other objects in the scene. Depending on who you ask and what software you use, global illumination may or may not include diffuse<->diffuse, specular<->diffuse or specular<->specular light transports.

Indirect diffuse light was the description we chose in FireFly to make sure it's an accurate description of what it does without raising unrealistic expectations. It calculates diffuse<->diffuse light transport through path tracing and irradiance caching (which can be turned off), but does not calculate caustic light paths which would require light transport through specular paths.