What is a one-person business called?

I'm wondering what is the term for the person, that is doing business on his/her own and has tax liability. It's different in each country, I'd like to know how they are called in USA and UK.

Solution 1:

Sole Proprietor: the person who owns and controls a sole proprietorship.

I am the sole proprietor of this business.

Or...

Independent Contractor: A person working independently, under a contract; a self-employed person.

I am an independent contractor.

Or...

Self-Employed (or Freelancer): working for yourself.

I am self-employed.
I am a freelancer.

Solution 2:

In Australia, they can be self-employed, freelancers, contractors, sole practitioners (for professional services), sole traders (for other services), and probably a lot more besides... I don't know if I have heard of sole proprietors here.