While I can appreciate the difference in definition between a made-to-scale startup and a more traditional business, I disagree that the former is "an entrepreneur" and the latter isn't. In fact, I'd argue that, if anything, it's the opposite. An entrepreneur builds a sustainable business. A "startup founder" is trying to strike oil.
These are very different things with different skills required, but, as the startup founder is the new thing here, it should get a new word instead of trying to force an existing, understood term to have a new meaning and just causing a lot of confusion as a result.