Chávena in Portugal. :)
Technically, 'a cup of coffee' (um café) in Portugal is actually a cup (shot) of espresso in the US, though of course there are other types of coffee drinks available.
But xícara is old Portuguese that fell into disuse last century in Portugal, and comes from Castilian (Spanish) via the Aztecs while chávena comes from Malay via the Chinese.
In the US, a xícara of coffee is traditionally served at home in a ceramic cup as opposed to a glass cup. Therefore we to differentiate a xícara from a copo we call it a "mug." You still would ask for a cup of coffee, but mug is a slang term for a ceramic cup as opposed to a paper cup.
Except mug in Portuguese is different, caneca.
Xicara is a cup, and in Portugal at least it is quite small, espresso coffee size often (when used for coffee). Chávena actually has the root of Chá in it so is more a teacup (in the English mind though used for all sorts of hot beverages in Portugal). Both are usually ceramic or porcelain. However, EU-PT while it used to use "xícara" rarely does now in favor of "chávena" for all cups with handles (except mugs). Copo is more a glass (without handle), though some cups are indeed made with glass (so they are clear) .
I do not think mug is a slang term in English.
But it would be somewhat odd indeed to be served coffee in a mug anywhere but at home (where tea often gets the mug treatment too):
Another difference is that in English a cup is also a measurement (8 ounces) while a mug is usually 12 ounces, or even more. Cups in Portugal tend to be smaller though but for recipes "chávena" is used as a measure.
according to Wiktionary, it seems a "cup" must have a handle, and a "glass" is made of some translucent material.
in US English, a "cup" is just a generic term for a drinkware regardless of whether it has a handle or not. a "glass" is generally a type of "cup". people say "can i get a cup/glass?", but "glass" is probably less frequently used and almost always refers to something translucent. you wouldn't call coffee drinkware, "glass". "teacup" is a specific type of drinkware, but it could also be just called a "cup". "wine glasses" are generally called "glass," but if they were stem-less, they could probably called "cup" as well.
if "xícara" is "cup" and "copo" is "glass," what's the word for styrofoam/paper "cup"? i don't care about the Portuguese word for styrofoam/paper; i'm asking what the general word for what you would call these kinds of "cups". OR does Portuguese specifically differentiate something by handle/no-handle? is the difference between "xícara" and "copo" a matter of material/shape/word choice?
hopefully somebody understands what i'm saying.
Not everything translated to English from a phrase using, "of" (de in Portuguese) will become a possessive (o gato dele/his cat). English uses many "of" phrases such as, "cup of coffee" and "United States of America" rather than America's United States. :)
I do not know why people voted you down though. People asking questions here should not be discouraged like this. It is exactly what the discussions are for here. :(