When a government creates a corporation, it does so by statute or by issuing a charter or a certificate, after which the corporation is an independent legal person in the eyes of the law.
The primary advantage of a for-profit corporation is that it provides the shareholders with a right to participate in the profits (by dividends) without any personal liability (the company absorbs the entire liability of the business).
A corporation is either profit-seeking or not-for-profit, the latter also known as society, not for profit corporation or association.
The wide concept of the term, to include profit-seeking and not-for-profits, is exhibited in the US Code, in Title 11 (re bankruptcy), Chapter 1, ¶101(9), which defines a corporation as:
"The term corporation includes (an) association having a power or privilege that a private corporation, but not an individual or a partnership, possesses; partnership association organized under a law that makes only the capital subscribed responsible for the debts of such association; joint-stock company; unincorporated company or association; or business trust; but does not include limited partnership. "