Was there another numbering system other than Köchel for classical music?

Answer 1

Köchel numbers apply only to the music of Mozart, since Mozart was the only composer whose works Köchel catalogued.

Some other composers' works have been catalogued by other scholars. For example, Schubert's music is identified by Deutsch numbers and Haydn's by Hoboken numbers.

Many composers identify their compositions by opus numbers (the word opus means work). Some use a different method, which may be just a title.