Although letters to indicate the level of styling can be applied in a haphazard manner by manufacturers, the original meaning of GTO and GTI would have been quite specific.
They are both extensions of GT (Gran Turismo, Grand Tourer), a high-performance car designed for long-distance driving. Any such car could be considered a grand tourer, but the traditional and most common body style is the coup� (two door) with either a two-seat or a 2+2 seat arrangement.
GTO (Gran Turismo Omologato, Homologated Grand Tourer) is a race car also produced as a road legal version to meet motorsport requirements.
GTI (Grand Tourer Injection) is predominantly applied to a fuel-injection engined car which does not bear any relationship to a true GT e.g. Volkswagen Golf GTI.