Both of these schools of medical philosophy are identified by their place of origin.  The Coan began on the island of Cos and its founding was attributed to Hippocrates of Cos.  The Cnidian school developed on the Cnidos peninsula, which juts into the Aegian Sea from the Turkish mainland just a few miles south of Cos.  The Cnidian school is older than the Coan and they coexisted for centuries.