Mohair comes from goats and is essentially similar to wool. All three are considered protein fibers and will all degrade if cleaned with a high pH substance. Cellulose - Cotton, Sisal , Coir, Sea Grass, Abaca, and Raffia all come from plants. Jute could also be considered in this group, but is commonly used in the backing of very few carpets. Cotton is rare and sometimes not associated with the others.
Sisal is the more popular and used to be popular as door-mat material.
The Sisal yarn with Sisal pattern, but most Sisal yarn will come in Sisal pattern. Coir, Sea Grass, Abaca, and Raffia will likely come in a Sisal pattern too, and many synthetic copy this style. Cotton will take longer to dry than Wool and will likely require the same type of cleaning. Sisal will shrink if it gets wet while Coir will expand. Some manufacturers will blend Sisal and Coir.