I am struggling to understand perhaps a very simple concept in Blender. There are materials which might have some diffuse coloring and a texture image, and there are also UV maps with their own images. Both can be applied to meshes or faces, but it seems that if a face has UV map then the material's texture is ignored and an image for UV map is picked.
If so, what is the use for a texture in a material if it is replaced by UV map's image?
EDIT: I've added some images to clarify the issue I have.
Case 1: a basic plane with material which has a texture, and no UV map. Diffuse color is applied, but material's texture is not.
Case 2: like above, but with reduced intensity of texture.
Case 3: Added UVmap and added image to the UVmap. Now I have texture, but not the diffuse color, and if UVmap was a different image, it would be picked regardless of texture set in the material.
So if I have UVmap image, what is the material texture for?