When a man wishes to become a chief of one of the Aiel clans, he must go to Rhuidean and walk through the glass-column ter'angreal to relive the history of the Aiel. Should he survive the experience, he is marked with a Dragon entwined about his left arm. It is this marking which designates him a chief.
The Car'a'carn is in turn marked by having a Dragon on each arm. Prior to Rand al'Thor, the Aiel have never had a Car'a'carn. It is unknown whether the Car'a'carn necessarily needs to also be He Who Comes With the Dawn.
The Car'a'carn is not the same as a king in one of the nations west of the Dragonwall. He is, at best, first among equals.