For me, there are two: denim and calico. It's true, cowboys were as likely to wear canvas or twill pants before Levis Strauss and Jacob Davis invented riveted jeans in 1873, but printed calico staked its claim in American fashions long before that. And both cotton fabrics have a long history before they became associated with the Old West.
Cotton has been cultivated and woven for at least 7,000 years in the Indus Valley (Pakistan) and Mexico. India developed a vital textile industry based on cotton. Through them, calico and muslin was introduced to Europe.
Natural calico (known as grey cloth in the trade) became known as muslin in America. What the English called muslin became finished muslin.
The devolution of the Indian textile industry by English and French trade sanctions, was capped off by American ingenuity. With the invention of the cotton gin by Ely Whitney, British, French and American mills could produce cheap cotton cloth and no longer relied on importing Indian calico and muslin.
Calico and muslin are simple weaves. There are others. Twill is a weave where pattern of diagonal parallel lines is created by "by passing the weft thread over one or more warp threads and then under two or more warp threads and so on, with a "step" or offset between rows to create the characteristic diagonal pattern." (Wikipedia) Serge is a specific pattern of twill which is very durable.
Jean, which takes it's name from Genoa (in French "Gene") is the same fabric and may be older than its French counterpart. Seventeenth century artwork has come to light showing common folk wearing clothes made of blue jean. (London Telegraph) Like our blue jeans, the cloth shows the indigo warp threads on the outside and the white weft threads on the inside.
Both calico and jeans are cotton fabrics, and both terms have evolved to mean more than material. Calico has come to mean the pattern, wherever it is used, as well as lending itself to calico cats and being used as a euphemism for women. Jeans are used to designate the pants made out of jean or denim. (However, denim jeans is a phrase that should be avoided.) Most of all (at least on this blog) they share a common bond in their connection to cowboys and their gals.
Wikipedia entries for Calico, Muslin, Worsted, Twill, Serge, Denim