Art music
The need for such terms came with the modern movement in the arts. Clearly the music of, say, Schonberg was serious, bur not classical in the sense of Bach and Beethoven. Stravinsky's music was a bridge between the two genres. It was classical music in part, and touched with African-influenced syncopations and dischords. So terms like "art music" and "modern music" were used by art critics and academics in their writing.