Entrepreneur: one who starts a new business. often several in sequence, regardless of whether the earlier ones succeed or fail. often with a new product, technology, market or competitive advantage. could start small then grow to very large, or, in some cases, start large at creation (think spinoffs or multi-corporate-backed partnerships.) May take VC. May become a billionaire. Often seeks an exit in the form of an IPO or buyout, and often early enough in their career that they can move on to the next startup, or, to retire young.
Small business owner: you own a small business. you may not have started it. you might have bought it. it might be a franchise. it often is not innovative. typically a commodity product or service (apples, hair cuts, lawn mowing, etc.). it often will not scale up well. it is often a family thing and may already be on the 2nd generation. if it fails the owner/founder is more likely to go back to having a traditional job. May take angels, but almost never VC. May become a millionaire. Often seeks to maintain it as a lifestyle business, at most offloading operational duties to hired management in order to gain a passive income stream, but typically closer to traditional retirement age.
in practice? the line blurs, esp when people use the terms without making a consistent distinction.
Steve Jobs: entrepreneur
Uncle Bob and his lawn moving service: small business owner, NOT an entrepreneur
(my two cents)