pg puts it well in one of his essayes: a startup is a company that solves a hard technical problem. The techical part is essential, not an afterthought. A fast-food chain would use tech, but it would not advance the art.
I would say that someone who wishes to get big, but doesn't take appropriate action, will still have a startup, albeit likely unsuccessful. You might define someone's company as not being a startup because you don't think they will be successful - but how do you know they won't be? Hence my ironic use of "delusional" etc. Many startups were doubted before they became successful.
http://www.paulgraham.com/wealth.html references the example to which I alluded: McDonald's.
A startup is a human institution designed to deliver a new product or service under conditions of extreme uncertainty.
http://startuplessonslearned.blogspot.com/2009/05/lean-start...
If I was to add anything to it, it would be something about 'ability to scale'.