Take a length of silk embroidery floss between finger and thumb and you can peel away one ply, then peel that ply thinner still. Try the same with cotton thread and it simply frays into fuzz. The difference is not skill or brand. It is that silk begins as a continuous filament hundreds of metres long, while cotton and wool begin as short fibres that must be twisted together before they hold at all.
A single cocoon filament is actually two filaments of fibroin laid side by side and glued with a gum called sericin. In reeling, warm water softens that gum, and the filaments from several cocoons are drawn off together and pressed into one strand of raw silk as the gum sets again. The result is one long, even, continuous thread — not a bundle of short ends held in place by friction.
Why length lets you go thin
Short-staple yarn has a minimum practical diameter. To make cotton stronger you add twist, and twist only works if there are enough fibres overlapping in every cross-section; thin the yarn too far and some cross-section contains too few fibres to hold the load. Silk has no such lower bound. A filament that runs the whole length of the thread needs almost no twist to carry tension, so it can be reeled very fine and still be pulled through cloth without breaking.
This is why embroidery floss can be divided. Several fine silk threads are laid together as plies, given only a gentle twist, and left as a bundle. Because the plies are not twisted hard into one another, a finger can separate them again. A cotton floss of the same apparent thickness has to be twisted tightly enough that pulling one ply apart just drags out loose fibre ends. The ability to split a thread is a direct consequence of not needing twist for strength.
The sheen is geometry
Fibroin is roughly triangular in cross-section rather than round, so each filament behaves a little like a prism. Light reflects off the flat faces with a directional bias, which is why a piece of silk embroidery looks lighter or darker as you turn it, and why two panels stitched in the same thread can appear to be different colours. Printers and weavers have used that property for centuries: change the direction of the stitch and you change the shade without changing the dye.
Then there is degumming. Raw silk still carries sericin, which makes it stiffer, duller and slightly yellow. Washing the gum away releases the individual filaments, softens the hand and brings up the lustre. The same material before and after scouring behaves like two different fibres, which is one reason fibre length decided what whole regions could wear and not just how fine their cloth looked.
Fine and smooth also means vulnerable. A continuous filament has no fuzzy ends to hide a snag, so a rough nail lifts a whole visible line. Alkali damages fibroin, and long exposure to strong light weakens it. That is why silk work is usually framed or lined, and why Guangdong's river-mud silk is finished on one face only — the treatment is part of the surface, not a wash that can be repeated.
The machinery downstream assumes the filament too. A drawloom lifts individual warp threads according to a stored pattern, and that only works cleanly when the warp is smooth, even and strong at a very small diameter. Fine silk made fine patterning possible; the patterning did not make the silk fine.
So the thread in your hand is doing three things at once. It is long enough to be thin, smooth enough to be split, and shaped in cross-section enough to catch the light. All three come back to the same starting fact: an insect spun a continuous line, and no one had to cut it into staples to make it usable.