There are two main types of companies: private companies and public companies. A private company restricts the transfer of shares and has between 2-200 members. It does not invite public investment. A public company has a minimum of 7 members with no limit, allows free transfer of shares, and can invite public investment. Some key privileges of a private company are fewer directors and membership requirements compared to a public company. The choice of business organization depends on factors like ownership, capital needs, liability, and regulation.