Think, not sure, but think that PA28Biggles' assertion is true only for Boeings...
see
www.airlinecodes.co.uk
There was a thread explaining Airbus codes but the search feature is disabled as I write this. From memory the A320 came as an A320-100 initially, BA inherited some - you can tell them from the absence of wing tip fences. Then Airbus produced the -200 with updates so that explains the 1st number. The second and third number refers to cabin and engine fit I believe. So it is I think possible to have two airlines with the same codes...