At least meteorologically speaking, typhoons are the same as hurricanes...which are the same as tropical cyclones. They're all the same intense tropical storms, they just get different names depending on what part of the world they form.
Hurricanes are not only the term used for such storms in the Atlantic Ocean, but also the Eastern Pacific Ocean. So storms that strike western Mexico and, yes, Hawaii are also called hurricanes.
Storms that strike the northern areas of the Western Pacific west of the International Dateline, like Japan, Taiwan, and the Philippines,etc. are called typhoons. Again, same storms, just different terms. (If a typhoon's wind speeds are over 150 mph, it gets the name "super typhoon.")
The similar storms that strike in the Indian Ocean and the Southern Pacific areas like Australia and New Zealand are "Cyclones."
Now there is a more generic term "tropical cyclone" -- if you look at some of the national wire stories, it'll mention Hawaii has been hit by 147 tropical cyclones since 1950 (but only three hurricanes!) -- that goes for any kind of cyclonic tropical-based storm. That would count hurricanes and tropical storms, but also tropical depressions and the like. For example, getting hit by a hurricane then a tropical depression would count as two tropical cyclones.
Can it be both?
Actually, yes! It's rare, but coincidentally, we have a current example. Hurricane Genevieve has been the forgotten storm of the trio in the Central Pacific but Thursady, the storm crossed the International Dateline and has been renamed Super Typhoon Genevieve (since its winds are over 150 mph -- a Category 5 on the Saffir-Simpson scale.)
Same name, but different
Now, while a storm bearing down on Hawaii and a storm that just flew by New England were both called hurricanes, there is a different list of names used between Atlantic hurricanes and Eastern Pacific hurricanes -- which explains why Hawaii is bracing for Iselle and Julio while the Atlantic coast is only up to the "B" name (Bertha -- just exited stage right from the Canadian Maritimes and is heading out to sea). The Eastern Pacific has been way more active so far this summer than the Atlantic.
** Atlantic Hurricane Names
** Eastern North Pacific Names
And yes, the Central North Pacific has its own list of hurricane names.
What about typhoon names? You can find their list here. It's works a bit different by not resetting each year, it just keeps going through the list until it has to start over again. We're at the name Halong now -- the bottom of the second list.
But no matter what you call them, they're all very dangerous storms!