Quantum computer vs classical computer application difference?

I understand that quantum computer operate completely different from classical computer in quantum level. But I don't seem to grasp the difference between those two in terms of application. Isn't quantum computer pretty much the same as really fast classical computer on the surface? If I program a software... show more I understand that quantum computer operate completely different from classical computer in quantum level. But I don't seem to grasp the difference between those two in terms of application. Isn't quantum computer pretty much the same as really fast classical computer on the surface? If I program a software on the quantum computer, wouldn't I be still typing alphabets and numbers? I wonder if I need to understand complex math to be quantum computer guru.
Update: Thanks everyone for all the insightful answers!
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