I think this is a good question, as it is an issue that is frequently misunderstood. There is an aromatic flavoring called angostura bark, though it seems to be more used in traditional medicine than in any food or cooking situation.
Angostura brand bitters, on the other hand, do not actually contain the bark at all--they are instead a brand--House of Angostura--named for Angostura, Venezuela.
As a flavor, this formula belongs to a class of bitters called "aromatic bitters" (as opposed to, say, orange bitters. Angostura is probably the best-selling brand of aromatic bitters, at least in the US, but they are by no means the only player. Fee Brothers and Peychaud's are both popular alternatives. Though there is a fairly wide variety among aromatic bitters, and their formulas are secret, they do have some commonalities. For example, gentian root tends to be the strongest flavor. They are also, as the name implies, very aromatic, so that a "dash" or two is plenty to flavor a drink.