Translation:One glass, please.
A コップ (koppu) is the general term to refer to a container/vessel used for drinks.
A カップ (kappu) is a コップ (kappu) with a handle used specifically for warm/hot drinks.
A グラス (gurasu) is a コップ (koppu) made from ガラス (garasu) referring to a cup without a handle used only for cold drinks.
I think very few Japanese people today would recognize those characters as meaning glasses/tumblers, since the katakana コップ is almost universally used. To most Japanese, "コップ". is simply a drinking vessel, whether it's made of glass, porcelain, plastic, or paper. Extra-thick drinking vessels (for hot drinks) are sometimes called マッグコップ.
On a side note, コップ presumably was derived from the Dutch. Between 1630 and 1854, the only Westerners who were allowed to trade with the Japanese were the Dutch, and even then, they were confined to a couple of small islands off the coast of Kyushu.
Okay so glass, is コップ. Then what is ガラス?！ You can't just say it's only the glass for windows and stuffs not the proper glass we drink water in it, because I have actually heard people saying コップ to cups, and ガラス to glasses. Can someone just explain this to me?! I really don't get it... Maybe I'm wrong?
～杯 fits better for glasses。一杯のコップ【いっぱいのコップ】