coma (n.1)
state of prolonged unconsciousness, 1640s, from Latinized form of Greek koma (genitive komatos) "deep sleep," of uncertain origin.
coma (n.2)
"head of a comet," 1765, from Latin coma, from Greek kome "hair of the head," of unknown origin. Earlier in English as a botanical term for a tuft of hairs (1660s).