cup: a vessel for drinking, and by extension the portion it holds that a person must drink
At its simplest this word names an ordinary drinking vessel, the kind you rinse out or fill with cold water. The New Testament writers use it that plainly, but they also lean on a rich picture that runs through the Hebrew Scriptures, where the cup handed to a person stands for the lot God has measured out to them. What is in the cup can be gladness and blessing, or it can be suffering and judgment, but either way it is theirs to drink.
That image gives the word most of its weight. Jesus speaks of a cup he must drink and asks whether it can pass from him, meaning the suffering appointed to him. In Revelation the cup is filled with the wine of God's anger, poured out on the guilty. And at the Last Supper the shared cup becomes the sign of the new covenant sealed in his blood.
All of these are the same word doing the same basic work: a vessel, and the drink inside it that a person takes to themselves. The four uses are not different words but one picture applied to blessing, to judgment, and to an appointed fate.