In games a Diffuse Map usually means the color texture. Also called an Albedo map.
This map generally only represents the base colors. If diffuse is the only map being used, light, shadow and highlights can be used to simulate the effects of more complex shaders. In such shaders, less to no lighting information is present in the diffuse, because those effects come from the contribution of other map types, such as Specular maps and/or Normal maps.
In offline rendering (movies, commercials, etc.) a diffuse map can mean a separate effect from a color map, where it controls the spread of any light that is being reflected off the surface.