That's the third time I've heard someone describe a fear of heights as a fear of falling. I also think it's funny that everyone who says that uses the same example - that they're fine in a plane. (Most people I know with a fear of heights do not have a fear of flying, so I don't really know where that comes from.)

I've never had a problem calling it a fear of heights, but I was taught in psychology that most people with phobias or anxieties about things don't commonly get it in every situation. Like a person with claustophobia isn't going to get the symptoms of it usually in every situation that involves small spaces, and people with anxiety disorder are usually classified in several different ways depending on where their anxiety pops up. And most people will get more than one situation that makes it pop up, but not every situation.