[Nicolai P. Zwar]

I use the terms context dependent. The best definition of general “classical music” I know is the one Leonard Bernstein used, that “classical music” is basically music written down in fixed form, that’s the (broad) main distinction, and puts it apart from jazz, folk, rock/pop, where the way the music is performed and the instruments used may very greatly from performer to performer.
So “classical music” is a continuation from earliest choral music to Bach to Beethoven to Boulez to Beyond…

Now if it’s a discussion within this field, it may make sense to distinguish between “Baroque”, “Viennese Classical”, “Romantic” periods etc., but to “outsiders”, that’s all the same anyway, grouped under “classical”.

I don’t particularly like the term “Western Art” music, as it doesn’t really distinguish anything (isn’t Jazz and Rock also “Western Art”?), though that’s just personal preference. The important thing is simply to be clear how one uses the terms in any context.
But the Bernstein definition is the most satisfying for me.