I basically agree with Guido, but I would modify his statement as follows (changes are in brackets):
Regards,
-- Al
... a warm sound is a tone that has a [lower] midrange preference, and perhaps a touch of pillowiness in the mid and mid lower bass. A rich sound for me has significant exposure of harmonics throughout the range, [particularly lower order even harmonics], from low bass to higher treble, without distortions.Of course, usage of these terms among different audiophiles varies widely, and sometimes they are used interchangeably. But strictly speaking, IMO, "warmth" relates to frequency response, and "rich" relates to harmonic balance.
Regards,
-- Al