Difference between texture and illumination in image
Very basically illumination refers to falling of light onto the objects and making them visible as they are illuminated, whereas texture is essentially geometric patterns on the surface of objects such as dots, lines, crosses, letters, symbols, figures etc. Hence they are two quite unrelated aspects of optical images, assuming the image is composed of objects and alike.

The subject of illumination is dealt within the science of photometry, in which light source characterisation, light radiation, interaction of objects with light that falls on them, and finally how humans perceive the resulting optical stimulus that comes into our eyes as reflections from our environment is studied primarily...