"Entrepreneur" implies more of an active risk-taker in business, whereas a "proprietor" of a business simply owns and operates it. (I've checked both dictionary.com and oxforddictionaries.com who say the same thing)
Well, you can be a stodgy, unimaginative non-risk-taking business owner, in which case you certainly wouldn't be an entrepreneur. But we'll add it as a type-in anyway.