Of course it matters, just like the difference between the words simmer, boil and steam matters. They're all methods of cooking with moisture, but they don't describe the same thing.
The definition of a hurricane includes where the originates and where it gets its energy - which is from the warm waters of the tropics. This is from DH: Once a hurricane goes up the coast, it's no longer fueled by warm water. It changes and mixes with other air masses and is no longer a hurricane, but more like a nor'easter. It can still be a s**t-kicking storm, but it's not a hurricane.
Anything with the word cyclone or typhoon in it certainly should give the impression of a dangerous storm. If it doesn't, well, lots of people use words without knowing what they mean.