Currently major structural elements make the most use of bismaleimide and epoxy thermosets. PEEK thermoplastics are gaining share. There's a lot of these and other resins; one of the best-known suppliers with good detail on their website is Cytek.
Thermoplastics can be melted away and are partially recycled for low performance uses. Thermosets are non-recyclable. This, along with lower cost processes, is among the drivers for thermoplastics growth.
Now that composites are the new norm, some expect the next materials advancement metric after composite % to be thermoplastics percentage. The point isn't so much resin recovery as the ease and thus likelihood of recycling.
The recovered fiber is chopped up further and used in bulk in low performance applications. Most consumer goods and aftermarket car parts advertised as carbon only use a layer of woven CF on the outside, with the thickness built up by fiberglass or chopped CF mats with resin matrix.
Short (microns) chopped fiber is also used to fill [thermo]plastics for conventional bulk plastic manufacturing processes. That can be found in cell phone chassis and plastic structural parts in consumer products.