This is an overview of how textiles can be categorized.

In the world of textiles, there are natural fibers and man-made fibers. Natural fibers are fairly easy to identify—cotton and wool for example, and can be further divided into protein based—animal sourced, and cellulose based—plant sourced. Man-made fibers include natural polymers—both protein based and cellulose based, biofabricated—usually lab grown materials, and synthetic polymers—anything with ‘poly’ in the name, plus nylon, acrylic, and on. Here’s a list in progress, compiled with information from The Sustainable Angle and Future Fabrics Expo.
For a look at alternative material resources, read Materials + Resources.

Protein Based: wool, cashmere, mohair, alpaca, camel, angora, vicuna, silk, yak
Recycled: recycled wool , recycled cashmere, recycled silk

Cellulose Based: cotton, linen, hemp, ramie, jute, nettle, pinatex, bamboo linen, banana fiber
Recycled: recycled cotton, recycled linen, pinatex

From Natural Polymers:
Protein + Bio-based: milk casein, collagen, seaweed, castor, corn, soy, pla/non-woven
Recycled: crab shell, food waste source, oyster shell

Cellulose Based: viscose, rayon, cupro, tencel lyocell, tencel modal, lenzin ecovero, lyocell, bamboo viscose, acetate, triacetate
Recycled: tencel with rifer tech, agraloop

Biofabricated: mycelium lab grown leather, mylo, lab grown collagen leather, zoa bioleather, by modern meadow, lab grown spider silk, amsilk from bolt threads, algae

From Synthetic Polymers: polyester, polyamide, polyurethane, polyethylene, polypropylene, nylon, pvc, elastane, acrylic, modacrylic
Recycled: recycled polyester, recycled nylon, recycled elastane, recycled p.e.t.
For a look at alternative material resources, read Materials + Resources.