Being from Louisiana, I too have had my share of hurricanes. With respect to your question, I believe you'll find that they are all the same thing. What you call it (hurricane, typhoon, or cylone) depends on where the storm is.
Cyclone is the more generic term, referring to any cyclonic (non-frontal) storm system that spins over tropical or sub-tropical waters, surrounded by organized thunderstorm activity, with clearly defined surface wind closed circulation.
To the specifics:
A Hurricane is a tropical cyclone in the North Atlantic (or the Gulf of Mexico), the Northeast Pacific east of the International dateline, or the South Pacific east of 160E longitude.
A Typhoon is a tropical cyclone in the Northwest Pacific, west of the International Date Line.
In the North Indian Ocean, a tropical cyclone is referred to as a "cyclonic storm", and in the Southwest Indian Ocean, it is simply known as a "tropical cyclone".
Good Luck
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