An image (2D) is the projection of a natural scene or man made drawing on to a plane. The output of an optical sensor when displayed is an image.
Texture is a picture created by repeating a basic element called 'texel'. The texel can be a natural image or an artificial one.
The edge detection algorithms works on matrices. So if it is a normal image or texture image, you can do in the same way.
In texture images, recognizing the texel makes the rest of processing easy. Because you need to work on a smaller sized matrix.