Viticulture is a branch of horticulture having to do specifically with the cultivation of grapes for winemaking. There are dozens of official American Viticultural Areas designated by the federal government, the overwhelming majority in California.
Although wine grapes are being grown in Vermont, there's no official AVA designation as of yet. In the U.S. the AVA is what gives a wine its appellation, or place name.
Certain requirements must be met in order to have a specific appellation appear on the label. For example, in a wine labeled “California pinot noir” the grapes could have come from anywhere in the state, while a wine labeled “Russian River Valley pinot noir” contains grapes grown only in that small Sonoma County region.
Vinification is, simply put, the process of making wine, primarily but not exclusively from grapes. Fermentation is essentially the process by which yeast acts on the sugars in juice to produce alcohol and carbon dioxide. Other factors also come into play when making wine, from filtering to barrel aging to fortifying.
And once it's in the bottle, wine continues to change over time - sometimes for not very long and sometimes over decades, depending on the wine.
In the movie Sideways, one character put it this way: “I like how wine continues to evolve, like if I opened a bottle of wine today it would taste different than if I'd opened it on any other day, because a bottle of wine is actually alive, and it's constantly evolving and gaining complexity. That is, until it peaks . . . and then it begins its steady, inevitable decline.”