What is the difference between a typhoon, cyclone, and hurricane?

They are different names for the same type of storm, collectively known as tropical cyclones.

What they’re called is determined by where they are form. In the Atlantic Basin and east of the International Date Line in the Pacific Ocean, they’re called hurricanes. Typhoons form in the North Pacific Ocean, west of the date line. The storms are called cyclones in the Indian Ocean and in the Coral Sea off northeastern Australia.