Interesting question. At an airport once, I met a small business consultant who was in the business of helping people start restaurants. He said he always recommended buying a franchise instead of thinking up their own idea. According to him, franchises have a 70% rate of success as opposed to 10% for made-from-scratch restaurants.

So nominally, the presence of an innovative element in the business idea, that requires searching for a market to some extent, instead of merely occupying an existing obvious one (such as by buying and taking over a business), is the difference.

This causes the 'greater risk factor' Andre mentions, but I wouldn't call 'greater risk' the main difference. There are some apparently entrepreneurial ventures that have far lower risk than very traditional 'business owning' activities. If you invented a cure for AIDS or time travel, you'd probably be safer than most coffee shop owners.

A twist to the tale is that so many self-styled entrepreneurs are so enamored of that label that they forget the basics of 'owning' (and running) a business. So they increase their risks just by viewing themselves in a more romanticized way that makes them prioritize things differently (eg. raising money over serving customers).