Taza can refer to a measuring cup, but it can also refer to a drinking cup. Generally speaking ...
Vaso - a glass - something you would likely serve water, juice, tea, or other cold beverages in
Taza - a cup - something that you would likely serve coffee, cocoa, or other hot beverages in, likely to have a handle, might be ceramic
Copa - a glass - something that you would serve wine or a mixed drink in, likely to have a stem (Also used colloquially to mean an alcoholic drink in the same way we say "can I buy you a drink" meaning booze.)
FULL DISCLOSURE: Native English speaker - US, Southern Appalachian dialect. Other uses of English may vary. Advice about Spanish should be taken with a grain of salt.
Does a "vaso" also need to be made of glass?
In English, I think "a glass" is always made of glass (or maybe transparent plastic to imitate glass). If you have the same thing but it's made of opaque plastic or paper, then it's called "a cup" (at least where I'm from).
(Also, where I'm from, a cup for hot drinks with a handle is called "a mug".)
If you have a "vaso", but it's made of opaque plastic or paper, is it still called "un vaso"?
On the very last question i got it wrong and the question was "un vaso de agua"...my translation was "a glass of water"...it dinged me and said the tanslation should have been "one glass of water"...i could have sworn the number one is translated as uno not un...and this was reinforced on this question when the the answer for "un vaso" is "a glass"...
I find it curious that, in English, people use the same basic word (glass, glasses) for the objects and the material they are made of, while in Spanish and Portuguese (my native language) we use words with such different forms and origins: Vidrio, vaso, gafas (Spanish) Vidro, copo, óculos (Portuguese)
It doesn't really matter. When in doubt asume it means a. A glass is the same as one glass. "Can I have one glass of milk" would be right, but nobody says that. "Can I have a table for a person" just sounds strange. Say it out loud both ways and decided which word you would use in English.
You were supposed to type what you heard. Not the transition. Your answer should have been "un vaso", which translates to "a glass", instead of the actual translation. It didn't mark you wrong for a lack of capitalization, it marked you wrong for answering in the wrong language. Next time read the instructions more carefully. :)
(Sorry for deleting my previous comment, I made a spelling mistake and I had to fix it).
una taza is a cup. un vaso is more like a glass (like a glass you drink from). Vaso is also something we call a "false cognate". A "cognate" is when a word is similar between two languages, like "inteligente" and "intelligent". Vaso is a "false cognate" because vaso doesn't refer to a vase, but rather a glass. I've never had to use the word vase in spanish, but I don't believe its actually vaso.
nc.chelle (above) laid out the distinctions very clearly and accurately. Vaso is usually translated as glass. Taza is a cup, as in a cup of tea. Copa is usually a stemmed glass, thus una copa de vino -- a glass of tea. These partial cognates can be confusing. If you memorize these phrases, you'll probably use the terms right in other contexts: Un vaso de leche. A glass of milk. Una taza de te. A cup of tea Una copa de vino. A glass of wine
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