Had this question been posted the other way around, the answer would have been far simpler! Strictly speaking, a business owner is the legal proprietor who is responsible for making a profit from the successful operations of the business. In many cases a business owner bought their way into an existing business, inherited the business, was employed by the business, or became an owner through a business transaction. In any event, the business owner may join the business 20 or more years into the business operations and not know anything about the initial start-up of the business.
Juxtaposed against this is the entrepreneur. An entrepreneur is someone with a particular mindset, who takes risks with their original business ideas, and very often move out of the business after the initial start-up phase. From a business coaching perspective there are significant differences in the behaviours and approaches that the entrepreneur takes, as opposed to the business owner.
So often, a business owner seeks stability, where the entrepreneur creates energy through seeking change. The business owner tends to make use of tried and tested methodologies, where the entrepreneur invents new techniques or technologies. Business owners often see their business as being part of their identity, whereas the entrepreneur itches to move on to the next exciting venture. Business owners seek profit, where entrepreneurs pursue their passions. Business owners flourish in stability and security, where entrepreneurs revel in change.
An entrepreneur may be a business owner, but it is very rare for a business owner to be an entrepreneur!