DS-2019 - A form given to exchange visitors in the U.S. on J-1 visas. This form is the document which shows the start and end date of your visit, program of study, finances and is issued by the school you are required to attend.
I-20 - A form given to individuals in the U.S. on F-1 student visas. This form is the document which shows the start and end date of your visit, program of study, finances and is issued by the school you are required to attend.
I-94 - An I-94 form is an official record of the entry a non-immigrant visa-holder into the United States. Along with biographical and passport information, this record contains the traveler’s the date of entry into the US, the status of admission into the US, and the duration of that status. Air and sea travelers will be issued I-94s during the admission process at the port of entry. You can print your I-94 from the U.S. Customs and Border Protection website (use Internet Explorer); click on "Get Most Recent I-94."
The I-94 is needed for employment paperwork (e.g. I-9 form) and employment authorization for visa-holders (e.g. OPT for F-1 students).
Visa - Your visa is the stamp in your passport that indicates the status under which you are permitted to enter the country. It is used ONLY for entry into the U.S. F or J visas cannot be renewed or extended within the US. An F or J visa does NOT indicate the length of time you are allowed to remain in the United States, as the length of stay is indicated on your I-94 document.