It is the location of the storms' occurrences. Hurricanes occur in the Atlantic ocean or east of the International Date Line, typhoons in the Pacific west of the International Date Line, and cyclones in the Indian ocean and south of the equator in the Pacific ocean.
All three are the SAME basic weather event. They are large scale (hundreds of miles across) and form initially over tropical warm sea areas; moist air over the warm sea being their energy source. Their winds are violent (with speeds of at least or 74 miles per hour (119 km/h)), with a circular movement round a central eye (30-60 km [20-40 mi] in diameter, with clear sky and no wind).
In the Northern hemisphere the rotation of the winds is counter-clockwise and south of the equator it is clockwise (the storms do not cross the equator).
Once the storms make landfall, they weaken because their energy source is cut off. When they hit land, the heavy rains and fierce winds cause severe structural damage and can cause flooding of streets and homes accompanied by landslips.
-- Hurricane: a violent tropical storm or wind, especially found in the West Atlantic Ocean.
-- Typhoon: a violent tropical storm or wind, especially found in the West Pacific Ocean.
-- Cyclone: a violent tropical storm or wind, especially found in the Southeast Pacific and Indian Oceans.
The word "cyclone" is also used to describe any low pressure weather system (the opposite of an anti-cyclone). The term cyclone therefore applies to virtually any large-scale low pressure system with cyclonic rotation, that is counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere.
Therefore, the term cyclone can be used to describe hurricanes, typhoons, tropical storms and tropical depressions (collectively known as tropical cyclones) as well as extra-tropical and polar lows. Although low pressure systems often bring rain and thunderstorms they are not necessarily violent or severe.
Therefore, technically, all hurricanes and Typhoons are "cyclones" but not all "cyclones" are Cyclones, Hurricanes or Typhoons, because the wind speeds are not fast enough.
*Incidentally, despite a popular misconception, cyclones are never called "willy-willies" in Australia. A willy-willy is a harmless whirlwind.
Also Tornadoes are not willy-willies, Cyclones, Hurricanes or Typhoons. They are structures formed by a single cloud and may have even faster wind speeds present over a smaller area.