Has the building got columns in front of it? Check. Has the music got lots of strings and horns? Check. Chances are both are classical — representative of a past culture.
Often classical describes anything from ancient Greek or Roman culture, because, boy, those guys were good. Be careful when using classical and classic; they're not exactly the same. While something classical is usually a classic, it doesn't necessarily work the other way around. A classic is something exceptional that we tend to judge in a different time frame. A classic rock album? Definitely not made by the ancient Greeks or Romans. So far as we know.