Gee. There are so many distinct types of drinkware in the Western world.

(Picture via http://goo.gl/IBnSd)

Rocks glass (a.k.a. old fashioned glass and lowball glass), table-glass, wine glass, shot glass, highball glass; mug, coffee cup; and on and on.

Personally I'm fond of rocks glass, table-glass, and mug. :-)