When we order a milkshake, we usually just ask for "a milkshake". We do not use glass or cup.
"I�ll have a large chocolate milkshake."
The only time we usually ask for a glass of something, especially when at a restaurant, is for a glass of wine.
When the waitress/waiter asks us what we want to drink, we usually answer- a coke, pepsi, coffee, tea, etc.
When ordering from a take out or drive through (like McDonald�s) we usually order a coke. They ask what size- small, medium, or large.
In America, we usually do not specifiy what the liquid should come in. We already assume that most things come in cups. Cold beverages come in one type of cup, and hot beverages come in cardboard or styrofoam cups.
Glass is for cold liquids (they break if hot liquid is poured into them) and cups or mugs are for hot liquids.