"We call a tropical system a hurricane in the Atlantic and northeast Pacific. In the northern Indian ocean, they're called cyclones. And people living along the northwest Pacific call these storms typhoons," according to AccuWeather.
Aside from where these storms take place, they all are the same weather phenomenon. The only time when a hurricane would become a typhoon is if the storm crossed the International Date Line at 180 degrees west longitude. This happened recently in 2014, when Hurricane Genevieve crossed this line and became Typhoon Genevieve.