These three words all describe the same phenomenon:
a tropical storm of fierce spiraling winds. Such storms occur around the world, but only between the equator and latitudes 30° north and south of it.
When these storms occur in the Atlantic Ocean, they are called hurricanes.
They are called cyclones in the Indian Ocean and typhoons in the Pacific Ocean. Cyclone is also a generic word for a whirlpool of wind.
In Australia, tropical storms of fierce spiraling winds are also known as willy-willies.