hurricane=typhoon=cyclone. it's a matter of geography.
the national hurricane center (US) tracks the the whole atlantic/carribean, gulf of mexico and the pacific out to 140 degrees west longitude in the northern hemisphere. Any storms that appear in that jurisdiction are known as "hurricanes"
anything in the northern hemisphere west of 140 is known by the chinese (original language i think) name of "typhoon" and anything in the southern hemisphere takes the british (because of australia and other british colonies in the area) name of "cyclone"
to further complicate matters, the blanket term for all these storms is "tropical cyclone" and the names listed above are regional terms.
to FURTHER complicate things, a "hurricane" can become a "typhoon" by crossing 140W. tracking of the storm is handed off from the US NHC to their asian equilivent.
a tropical cyclone can NOT cross into the southern hemisphere from the northern one though. the corriolis force that gives the cyclones their spin reverses, and would tear the storm appart. cyclones in the southern hemisphere spin clockwise, while cyclones in the northern hemisphere spin COUNTER clockwise.
does your head hurt yet?
edited to correct the spin direction