Most synesthetes are associators: the color triggered by a chord is vivid, specific, and automatic, but it happens on an inner screen rather than out in the room. Associators sometimes hesitate to call themselves synesthetes at all, assuming the projected version is the real thing.
Consistency testing treats both kinds identically, and associators pass it just as strongly. The projector and associator labels describe where the experience lives, not how genuine it is.
Self-report scales like the coloring of inner speech distinguish the two, and imaging studies hunt for what differs in the pathway.