So in the interest of Multioceanic equality we should
name the storms, #1. Hurricane Ann, #2. Cyclone Bill,
#3. Typhoon Cindy......repeat.
I actually prefer Typhoon, although Divine Wind comes a
close second.
LOL.
FWIW, your NOAA site has the answer, belle rouge...
What is a Hurricane?
A hurricane is a type of tropical cyclone, which is a generic term for a low pressure system that generally forms in the tropics. The cyclone is accompanied by thunderstorms and, in the Northern Hemisphere, a counterclockwise circulation of winds near the earth's surface. Tropical cyclones are classified as follows:
...Tropical Depression
...Tropical Storm
...Hurricane
So, all hurricanes are cyclones, not all cyclones are hurricanes. And the 'hurricanes' out in the Pacific are called typhoons or willy willies.
See
http://www.nhc.noaa.gov/HAW2/english/basics.shtml