In the United States, a person running a business as a sole proprietorship or a limited liability company is considered self-employed for tax purposes, but the sole shareholder of an S Corporation is not considered self-employed. Such a person is considered an employee of the corporation and does not pay self-employment tax, but instead pays FICA tax (matched by the corporation) at half the tax rate at which the self-employment tax is imposed -- 7.65% each by employer and corporation, instead of the 15.3% self-employment tax.
A home business (or "home-based business" or "HBB") is a small business which operates from the business owner's home office (SOHO).