Hi Mattie Interesting question!
I actually think you can be all three at the same time. In my mind/understanding:
A business owner is just that - someone who owns a business.
An entrepreneur is someone who is working on setting up a new business and is responsible for whatever risks go along with the new venture.
And a freelancer is someone who works for clients without a long term commitment - ie - a freelance web designer will design websites for many clients over time, not just exclusively for one client.

The best part about all three is that you get to decide who you work with and what kind of projects/business you take on

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