It is very important to clarify two legal terms in order to fully understand how to maintain your legal status in the US. People are often confused about the terms "visa" and "immigration status".
A visa can not be extended within the US. You can only renew it at US embassy outside the US. However, it is not necessary to do so if you have no plans to travel overseas.
Visa
The visa stamp in your passport was obtained at a US embassy or consulate abroad and is used for entering the US. The visa shows the latest date on which you can apply to enter this country. It does not show how long you can stay here. When arriving at the US "port of entry," the US Immigration inspector examines your passport, your visa, and your Certificate of Eligibility (I-20 or DS-2019), and determines whether you are admissible to the United States. The visa functions as a key to enter the US. Once you have opened the door and entered, you do not need to worry about whether your visa is valid or expired. When you are leaving and need to re-enter the US, you must be sure that you have a valid key (US visa) for return. Note: Canadian citizens are not required to have a passport (if entering the US from within the Western hemisphere) or visa, but they must show their DS-2019 or I-20 and proof of Canadian citizenship at the US port of entry.
Immigration Status
After the immigration inspector at the port of entry determines you are admissible to the US, an immigration status is granted, which is shown on your I-94 card and your I-20 (for F-1) or DS-2019 (for J-1). (Most of you have either an F-1 or J-1 student status, or J-1 visiting scholar status). In most situations, your visa type and immigration status are the same, unless you have changed your immigration status after entering the US. For instance, some F-1 students changed their status to F-2 (the dependent of F-1 student) or to another temporary immigration status. To maintain your legal status in the US, check your immigration documents such as I-20, DS-2019 and I-94 card (not the visa stamp in your passport) and be sure to register full-time. For F-1 students, check the ending date under item 5 on your I-20 Form. For J-1 students and scholars, check item 3 on your DS-2019 Form.
Fuente:
Visa vs. Immigration Status
http://www.oiss.yale.edu/visa/visavsimmi.htm
