This can be a bit confusing because in Spanish you say the same thing for both of the expressions above: "copa de vino". If you go to a restaurant you need to say "I would like a GLASS OF WINE". You can not use "wine glass" because then you are just asking for the glass but with nothing in it! There are lots more restaurant vocabulary issues that you need to be careful with so "keep an eye out" for our future posts.
I hope that helps!
Soy el director de Daniel Smith + Partners. Tengo más de 10 años de experiencia enseñando inglés a españoles.