“coffee cup” is a semi-standard unit just like the ones you listed are. And yes, it’s about 6 fluid ounces, and no, nobody in the real world means “i drank 6 fluid ounces of coffee” when they say “i had a cup of coffee”.
That's what led me down this path. Searching the internet for "how much caffeine is in a cup of coffee" leads to the question of "what is a cup?", "how did you brew it?", "what kind of grounds did you use?".
Overloading is fun!