How are hurricanes, typhoons, and tropical cyclones related?
They are all the same thing.
Tropical cyclones can be either hurricanes or typhoons, dependent entirely on where they formed.
Tropical cyclones that form in the Atlantic Ocean or in the North East Pacific Ocean are called hurricanes. Tropical cyclones that originate in the North West Pacific.
Due to the fact that the North West Pacific has more warm water, there tends to be more typhoons than hurricanes in any give year, and they tend to be more violent in nature. This is just a tendency and should not be taken to mean that typhoons are always more violent than hurricanes.