I heard two expressions are employed to refer to the cup or mug that we use when brushing our teeth, tooth mug and tooth glass. My question is if tooth glass can be used to refer to the kind of cup made by something non-glass, for example plastics, or if tooth glass has to be made by glass?
Yes, it can. The material of the "tooth glass" will generally be transparent. "Glass" is still used in the names of lots of items in whose construction glass has been replaced with, most usually, plastics.
A 'beaker' normally has a 'beak' or protrusion on its lip, used for pouring its contents. If the lip is uniformly round, I would stick to 'tooth glass'.