Originally Posted by IAN-UK

Back last century there was a move by IATA to enforce the use of three-letter airline designators. It wasn't a popular move and has been repeatedly shoved to one side. Motivation was the exhaustion of unique two-letter codes: duplication of two-letter codes was allowed where airlines operated in distinctly separate geographical zones, and codes were (and are) reallocated some months after an airline goes bust. Against a shift from two-letters to three-letters was cost and loss of brand etc

ICAO has operated a three-letter system since way back, giving a unique identity to operators (not only IATA member airlines). So all IATA carriers have both codes, but many other airlines use three-letter ICAO codes. Some airlines grabbed marketable designators - Tap Air Portugal is TP or TAP. Others were less fortunate: LH - DLH.