Looks to me like an underdress or part of a set. I'd have guessed the same age that Nicole suggests.
Taffeta is a weave. Silk is a fiber. Taffeta can be made of silk, or it can be made of any number of other fibers, usually acetate.
So something can be silk satin, silk charmeuse, silk chiffon, silk velvet, silk taffeta, etc.
Likewise velvet can be made of silk, or cotton, or rayon, or a mixture of these.
I can see why people say it looks like polished cotton. It does. But it also looks like it could be silk or a silk/cotton blend.