I think they are one and the same thing to my own understanding a person who owns and runs his own personal business can be safeThe owner of a business, for instance, may hire employees and essentially become the boss—an employee-owner who operates and manages the business. Independent contractors, sole proprietors of businesses, and individuals joined in a partnership are all self-employed persons.
to say that he is self-employed and also a business owner I don't really think there's a difference.