"Copo" is a simple cylindrical drinking utensil, which can be made of glass, paper, plastic, metal, where we serve most beverages.
"Xícara" has a handle and is usually small and bowl shaped, used for tea and coffee
"Caneca" is pretty much a Copo with a handle. Usually used for hot beverages and associated with the English word "mug"
"Taça" is what you drink wine from.