Pattern exists in nature as well as in designed objects; it is useful to look at the parallels. A Harvard biologist named Peter S. Stevens has published a book entitled "Patterns in Nature" in which he claims that there are only a finite number of ways that patterns can be structured. He starts with the idea of a grid as the foundation for any structure or image. He presents a set of ways in which the points of a grid can be connected. These modes of connection become classes of pattern, which he claims can be seen in any situation, in nature and in made images, and from the microscopic to the cosmic scale.
The modes he describes include the following which are described here in terms of examples from nature. However, each of these modes can also be seen in examples of designed objects and works of art:
Flow All things flow, following paths of least resistance. Flow can be seen in water, stone, the growth of trees. Meander patterning is related to the idea of flow, and is built on the repetition of an undulating line. In this detail from a textile hanging made up of knotted threads, the meandering color lines resulting from the technique quite naturally create this type of pattern.
Branching is an obvious form of patterning in the plant world, but it can also be seen in geological formations such as river deltas and certain crystalline formations.
Spiral patterns can be seen from the scale of galaxies to the opening "fiddlehead" buds of ferns, to the forms of microscopic animals.
Packing and Cracking refers to the way in which compacted cells define each others shape. A densely packed cluster of mushrooms will grow together, deforming the circular form of each cap because of crowding. In the same way a cluster of soap bubbles deforms each bubble from the perfect sphere of the isolated bubble, according to rules that govern the surface tension of soap bubbles. Surfaces (like mud or old paint) that shrink may experience cracking, resulting in similarly cellular patterning.
Similar types of patterning can be seen in many designed objects. Even complex works of art exhibit an underlying structure or pattern grid, although the mode of patterning may vary over the surface of a complex composition. For a site that goes into the mathematics as well as the art in patterns, try this link to a site that discusses the tiling theory in Escher's prints.
Textures are of many kinds:
Bristly, rough, and hard -- this is what we usually think of as texture, but texture can also be smooth, cold and hard , too. Smooth, soft, and/or warm and Wet or dry are also textures; in fact, any tactile sensation we can imagine is a texture
In other words, all surfaces can be described in terms of texture. Many artists and designers make use of texture as a dominant element in their work. This is particularly evident in craft media, such as fibers, metal, wood and glass, where the tactile qualities of the material are a major feature.
Creation of the illusion of texture is also an important element in many paintings, drawings, textile designs, and other surface designs. This can be observed and discussed separately from the tactile qualities of the actual materials and surface of the work.
This link will take you to a good discussion of Texture and design.