“Classical Music” is a catchall term for any art music which is non-popular (in the sense of “people’s” or “folk” music). It applies to symphonic, vocal, and chamber (small ensemble) music.
In a finer, better world, “classical music” would mean the music of the Classical Period, which ranges from Franz Josef Haydn in the latter part of the 18th century to about the time Beethoven composed the Third Symphony, which ushered in the Romantic Era, shortly after the turn of the 19th.
Before the Classical Period you had the Baroque Period (Buxtehude, J.S. Bach, Handel), and the Renaissance before that (musical terms coincide with art history terms). Beethoven bridged Classical to Romantic. Other early Romantics included Schubert, Schumann, Chopin and Berlioz.
After Wagner everything changed…Late Romantics were either heavily influenced by Wagner (Bruckner, Mahler) or rebelled against him. The Nationalists depended on folk melodies and rhythms from their respective countries…Grieg in Norway, Sibelius in Finland, Smetana in Moravia, etc.
By the early 20th Century Modernism arrived, and everything went to pot. Stravinsky went one way (several in fact), Debussy and Ravel went another, Schoenberg started up the Second Viennese School and invented Serialism.
A Sonata is a musical form, a composition in three or four movements (usually alternating Fast/Kinda Slow/Slow/Really Fast) for solo instrument, often accompanied by piano. A Symphony is just a Sonata in Symphonic form.
A Suite is a series of dances, often ballet music rearranged into a piece that can be played in concert.
A John Williams composition would be movie music. That’s a whole nother kettle of fish. Movie music, as you know, started off with a guy banging a piano to accompany silent films. As the sound era started, film composers like Max Steiner and Franz Korngold drew heavily on European music to write mood music to accompany various scenes. As the 20th century progressed, composers like Bernard Herrmann and Elmer Bernstein became more adventurous…composers like Williams are actually reactionary, looking back to the popular film music styles of the '30s and '40s.