"Corporation" has a specific legal meaning in the United States and probably elsewhere, sometimes indicated by the abbreviation "Inc." or "Corp." or, in England, "Ltd." (In the United States the precise legal details would actually be different in every state!) It means a limited liability corporation, with special legal status--underlined recently by some controversial Supreme Court rulings. All of the others just mean "a business," and which is used depends on context, tradition, and fashion in an imprecise way. If the business is law or accounting, the usual word is "firm." HIstorically, "company" just means group of people, and can be understood by imagining the growth of a small business. Perhaps it starts out just by using the name of the sole proprietor, "John Doe." Then the sons enter the business, and it becomes "John Doe & Sons." Then they hire some more unrelated people, and it becomes "John Doe & Company." The "and" is a little old-fashioned, and it becomes "The John Doe Company," or "John Doe Co." Then the fashions change and it becomes "Doeco" or "JDCO International Synergistics." Boeing is a giant corporation whose official name is still "The Boeing Company." "Enterprise" is a somewhat elevated word, not the most usual way to speak of a company. (Although it sometimes occurs within a company name, "Doe Enterprises," implying that the Doe corporation has more than one business.)