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.
Definitions of classical
adjective
of or relating to the most highly developed stage of an earlier civilisation and its culture