Stockings were originally made from woven cloth. Knitting them was a huge improvement. The knit stitch that is all smooth Vs on one side (as above) is called Stockinette because it was used to make stockings.
The stitch that is known as Garter Stitch was used at the top of the stocking, like a garter, thus the name. It lies flat, stretches and recovers pretty well, for being centuries before the invention of elastic.