Hallo Barnowl,
Mr Köchel's attempt was to arrange Mozart's works in chronological order, but it was sometimes sheer guesswork regarding the actual dates of many of the compositions written prior to 1784.
Understandably people who came along later dffered and there had to be subsequent listings, the 3rd by the musicologist Alfred Einstein (1937), - people easily confuse him with the Father of the Relativity theory! - and the sixth by Franz Giegling, Gerd Sievers and Alexander Weinmann (1964).
Not to totally wipe off the Original KV numberings, but yet to maintain a more accurate chronological sequence, the Numbers were changed and letters were added - like a, b, c.......i......t etc. Sometimes the alphabets even doubled up- like ss.
Koechel's original list (K1) showing KV331 now shows up as 300i in the sixth revision (K6). Nothing to do with KV300 - which is a dance piece.
Interstingly, with the Köchel Numbers and some simple arithmetic, one can get a rough idea of when Mozart wrote a particular work. Take any KN above 100, divide it by 25 and add 10. This will give Mozart's rough age when he composed the piece. In your current particular piece, 331 divided by 25 = 13.25 plus 10 = just over 23 years of age. The K 6 revision puts the age as 12 + 10 = 22 years.
Hence the numbering difference.
Add the age to Mozart's year of birth - 1756. It will give a fair idea of the year.
Warm Regards
Prof K S (Mohan Narayanan)
Musicologist, Teacher
Chennai, India