1) A word that has two or more different meanings yet is spelled exactly the same way.
2) A word that might have multiple meanings. The medieval poet Chaucer was famous for this.
Explanation sentance: That roller coaster Ghostrider at Knotts Berry Farm is sick, I just love all the twists and turns.
vs. I got so sick on that roller coaster ride.
Explanation: In the first case, sick is used to emphasize how great something is. In the second sentence it is used in a negative connotation as to how one actually feels as in being sick to one's stomach.
Since sick has two completely different meanings, I would label it as a homomorph.