Yes, bourbon is a type of whiskey, but the two words are not interchangeable. The differences are subtle, but they are there; and any true whiskey or bourbon snob would know them.
Bourbon and whiskey are made essentially the same way, being distilled and aged in barrels. The major distinction is that bourbon must be made with 51% corn, while whiskeys can be made mostly of rye, wheat or malt. Bourbon must be made in the United States and matured in new, charred oak barrels to earn its name, but it does not have to be produced in Bourbon County, Kentucky; although, that is where much of our bourbon is distilled.
These standards are actually set in United States law, so you better know them!