I think pattern have a lot of different meaning and be used in many fields, but they all have a same concept. Pattern has the structures in a consistent, and regular manner. For example, Business can identify data pattern, like their sale and learn adapt based on it. However, pattern can also be described as a repeating element in a form of shape or form, with the combination of lines, points, and planes. It has an echo and rhythm element. It is designed to look parallel, and have a structure. Having a pattern are not just having the same plane and line, but it also works with the color. Patterns are commonly used in painting or drawing to add an interesting element in a composition.
Texture, I think can be used to describe the feeling and physical elements of the certain object. Most of the time we described the texture when we describe the food that we are eating, or what we are touching with our hands. Its used to describe the surface quality of the work. It is an element in two and three dimensional designs, and in how we perceived the physical element of the object or properties. For example if there is a bump, or something is standing out, it can be described as bumpy, rough, or uneven.
This illustration explains both the pattern and texture. It has the repetitive elements in the pattern. The line and the plane are all facing the same direction. The individual plane have six sided which made up of 6 lines. It also has a parallel to the surface texture. Just looking at the picture, you can see the middle individual plane have split in the middle making it feel like the surface quality is rough, and you can feel it if you run your hand over it.