Differentiation
A business owner is the boss within a clearly defined business. When I think of a business owner, a picture comes to mind of a small to medium sized business. The owner is the one who makes the decisions, and the business is probably going to end with him or her (or be inherited by someone in their family). An independent lobster fisherman who hires two or four people to help him on his boat during lobster season is a business owner. A hairstylist who opens her own shop and rents three stalls to other stylists (or hires them) is also a business owner.
An entrepreneur is usually seen as taking on greater risks than your typical owner. They tackle challenging situations and solve problems that are part art and part science. What they do will certainly overlap with an owner, especially early in the business. The entrepreneur invests money that they gather from their own resources, investors, the bank, and wherever they can find the people that they need. The biggest difference between a business owner and an entrepreneur is that the entrepreneur has a long-term view that is focused on systematizing, growing, and then selling the business for a profit. A hairstylist who opens her own shop, and then creates a system for hair and beauty related services that she develops into a chain of spas across the country, is an entrepreneur.
If you want to be a freelancer because you are a great writer, editor, artist, consultant, accountant, etc., then be a freelancer. Working as a freelancer is a great way to operate as a business, and to keep the freedom that freelancing and self-employment promise.

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