Not sure the exact def or wording but from my experience when i say bright, i think of the treble being a little higher and clearer. Sometimes listening to higher treble can be fatiguing.

Warm to me means more even sounding, no one aspect of the sound stands out. Ok so i don't really know how to explain warm.

One person said it to me, if you go to an underground club that plays trance and techno, the sound is bright because the music makes use of a lot of treble/higher pitches. In an opera or classical music place, the sound is more finesse or calming. I dunno, that made sense to me. Its like comparing Sarah Brightman to Kylie Minogue.

Sorry if i absolutely made no sense.