These words are interchangeable in the sense of "lying flat," "level with the ground or other surface." They differ, however, in certain literal and figurative applications. Prostrate means "reduced to weakness," "helpless," "exhausted," "overcome": "The exhausted hikers sprawled prostrate by the stream." "That stretch of countryside was left prostrate by enemy shelling." Prone indicates a face-down position, not solely a horizontal one. A supine position is one in which a person lies face upward. Prone also has a common meaning of "inclined toward," "having a natural tendency or disposition": "This worker is accident-prone." Supine has the additional meanings of "passive," "indifferent," "inactive": "Jailed persons tend to become supine after a long stay in prison."
Dictionary of problem words and expressions. Harry Shaw. 1975.