As I recall, the 2 and 3 letter airline (and the 3 letter airport codes, but not the 4 letter) are put together by IATA. ICAO does the 4 letter airport codes.
They are universally accepted by all the airlines, travel industry and the rest of aviation, plus all govt regulatory authorities such as Transport Ministries, DOT, etc.
The codes for the stock exchange are not accepted nor used out of that context, so stock trading and the SEC is about all you see them used for.
The CAL crew made a bad mistake, but not one that hasn't been made by many experienced crews from airlines all over the world, unfortunately. Complacency and thinking it can't happen to you are your enemies here.