Wool on wool (wool pile and wool warps and wefts): This is generally the least expensive type of carpet, but often the most “authentic” if such a word can be used. Wool on wool carpets have been made much longer and use more traditional designs than the other types of carpets. Because wool cannot be spun finely, the knot count is often not very high, compared to wool on cotton and silk on silk. High knot count is also not necessary for wool on wool carpets because they are often traditional geometric designs, or otherwise non-intricate patterns.
Wool on cotton (wool pile on cotton warps and wefts): This type of carpet can be much more intricate than wool on wool carpets because cotton can be spun finely and the knot count is generally much higher. In wool on cotton rugs, floral designs etc. are also found, in addition to the geometric patterns.
Silk on silk (silk pile on silk warps and wefts): This is the most intricate type of carpet with very fine weave. Knot count for silk carpets intended for floor coverings should be no greater than 100 knots per square cm, or 10 X 10 cm² and can be as fine as 28 X 28 knots/cm². Any carpet woven with the knot count greater than 10 X 10 knots/cm² should only be used as a wall or pillow tapestry. These very fine, intricately woven carpets are no larger than 3m X 3m. Resource : Wikipedia