I grew up wearing nylons. They were never silk stockings. By the time I was old enough for them, silk stockings were definitely a thing of the past and nylon stockings ruled. According to an article at American WWII.com, rayon was used as a substitute for a time but they didn't fit well and tended to sag and "form knees of their own."
A team of researchers at DuPont worked for a decade to find a suitable solution. One day Julian Hill pulled a rod out of a mixture of coal tar, water, and alcohol to find a filament stretched between the rod and the solution. Voila! Nylon!
The first nylon stockings hit the shelves in New York City in May, 1940. Of course once the war began, nylon went into use mostly for parachutes, ropes, and tires for the military.
The nylon stockings of the 40s and 50s had a seam running up the back of them that was always a challenge to keep straight. I remember in the early days of my teens, some girls just used an eyebrow pencil on the back of their legs to make it appear that they had stockings on. The "seams" stayed a lot straighter if you had a steady hand.
It wasn't long before garter belts (except for the fancy Victoria Secret type) were a thing of the past and, with the discovery of lycra, pantyhose became the popular norm.