The Bureau of Alcohol, Tobacco and Firearms (ATF) started establishing viticultural areas in 1978, and their regulation became mandatory in 1983.
All American viticultural areas were established by ATF until 2003 and are now determined by the Tax and Trade Bureau (TTB) of the U.S. Treasury Department. If a wine is labeled with a viticultural area, at least 85% of the grapes used to produce that wine must have come from within the viticultural area.
They're not the same. A viticultural area is a subset of appellation. It's just one kind of appellation. An appellation can also be the name of a country, a state (such as California) or a county (such as Napa County).
A viticultural area can be very small (such as Mendocino County's Cole Ranch AVA—150 acres) or very large (such as the Ohio River Valley AVA which includes all of Indiana, Kentucky, Ohio and West Virginia.) In Napa County they range from the largest (Napa Valley—25,280 acres) to the smallest (Stags Leap District—2,700 acres)
(Map courtesy of Napa Valley Vintners Association.)
Atlas Peak—11,400 acres
Chiles Valley District—6,000 acres
Diamond Mountain—5,000 acres
Howell Mountain—14,080 acres
Los Carneros (located in both Napa and Sonoma Counties)—36,900 acres
Mount Veeder—15,000 acres
Napa Valley—225,280 acres
Oak Knoll District—8,300 acres
Oakville—5,760 acres
Rutherford—6,650 acres
Saint Helena—9,060 acres
Spring Mountain District—8,600 acres
Stags Leap District—2,700 acres
Wild Horse Valley (located in both Napa and Solano Counties)—3,300 acres
Yountville—8,260 acres