Company
A company is any entity that engages in business.
Corporation
Corporations are different from other types of company in that they exist separately from their legal owners. That means that liability is separate as well. With corporations, liability is limited to the holding of shares. In fact, shareholding is a major difference between corporations and other types of companies. With corporations, the shareholders each own a small piece of the larger corporate structure. Most companies are typically owned by one or a small handful of people, while corporations can be owned by thousands of different individuals.