A start-up doesn't necessarily have to be a webapp or even in the technology space. I believe any new business that could disrupt the status quo in an industry to the benefit of customers could be called a startup. In it's early days, Dell was considered a startup because of its disruptive distribution system, not necessarily the technology.
I think the question should be more precise. What's an _internet_ startup and what's a webapp?
A web app is another form of software distribution, via the web.