Muslin, percale and sateen refer to weave of material.
Supima and Pima are types of cotton textiles.
Thus you can have percale sheets made from pima, Supima, combed, Egyptian, Sea Island, or whatever cotton fabric.
https://en.wikipedia.org/wiki/Supima
https://sewport.com/fabrics-directory/supima-cotton-fabric
Muslin refers to cotton textiles with weave up to 144 threads per square inch.
Percale refers to cotton textiles with weave starting at or above 200 threads per square inch.
Upper limit for percale is about 320 or so threads per square inch. When you see bed linens like sheets with insane thread counts like 600 threads per square inch it means thinner cotton threads were used and doubled up. This higher thread count does not automatically translate into a longer wearing sheet or whatever. In fact since thinner threads were used it can mean things won't last as long.
Muslin bed linen was once the standard for middle class homes, hospitals, military, institutions, etc... Upper class homes still clung to fine linen imported from Europe for their bed linen. In early part of last century Wamsutta set out to change that....
Wamsutta Mills began marking a higher thread count percale with special patented weaving technology (equal tension or some such), that produced luxurious cotton bed linen which were long wearing and far easier to care for than linen. Other mills soon followed suit releasing and promoting their own percale bed linens.
WWII slowed things down, but by post war years percale came to displace muslin in most homes for bed linen. Where it was still used it was "economy" for homes that couldn't afford percale. However truth to tell, and as Wamsutta often pointed out percale saved money in long run.
Muslin bed linen owing to thicker threads are heavy, absorb lots of water, and thus take ages to dry. Those reasons also made ironing by hand or mangle difficult as well. For households or institutions that sent out washing it was normally charged by the pound, thus heavy bed linen cost more than lighter....
Because percale is a tighter weave than muslin it actually last longer even though threads may be slightly thinner.
Have tons of vintage Pequot muslin sheets and pillow cases in my stash, and have grown to hate the things for many of reasons listed above. Ironing even on a mangle takes knowing how dry things must be to get good results, but not so much so they will scorch. Am seriously considering gifting the lot to a cousin who has a wife just starting out in housekeeping.