A visa is issued by a US embassy or consulate and is stamped in your passport. It determines when and how you can enter the United States.

Your stay is controlled by the type of visa that you have, and is how long you may actually be physically present in the United States in whatever status your visa gives you. For example, B2 visitors are normally given six months. US CBP use to issue paper I-94 cards on entry, but now they just stamp your passport. If you need your I-94 to prove your stay, you must download it here.