Generally, a company is a form of business organization. The precise definition varies.
In the United States, a company is a corporation—or, less commonly, an association, partnership, or union—that carries on an industrial enterprise." Generally, a company may be a "corporation, partnership, association, joint-stock company, trust, fund, or organized group of persons, whether incorporated or not, and (in an official capacity) any receiver, trustee in bankruptcy, or similar official, or liquidating agent, for any of the foregoing."
In English law, and therefore in the Commonwealth realms, a company is a form of body corporate or corporation, generally registered under the Companies Acts or similar legislation. It does not include a partnership or any other unincorporated group of persons.