What is the difference between a visa and a visa stamp?
A visa is best defined as the right to be present in the U.S. for a specific period of time for a specific purpose. Both the type of visa on which a foreign national is present in the U.S. and the length of time during which that foreign national is permitted to remain in the U.S. are governed by the I-94 card.
The I-94 card may be either a white card which is stamped, noted with an expiration date and stapled into a passport upon entry, or a printed section at the bottom of a U.S. Citizenship and Immigration Service-issued Approval Notice (the white card will be light green in the case of a Visa Waiver Program entry for a short-term visit). With few exceptions (parolees, asylees and refugees among them), any foreign national in the U.S. who is not a permanent resident must have a non-immigrant visa to be legally present.
A visa stamp is best described as a "pass" or "ticket" to enter the U.S. It is reviewed upon entry to determine admissibility, but does not control U.S. status.
Can a foreign national remain in the U.S. if the visa stamp expires?
Yes, as long as the I-94 remains valid (unexpired). However, if the foreign national travels abroad, he or she will need to apply for a new stamp at a U.S. embassy or consulate before returning to the U.S.