A closely held corporation is a corporation in which more than half of the shares are held by fewer than 5 individuals. Closely held corporations are private companies, and are not publicly held. In a closely held corporation, if one of the shareholders wants to sell some or all of his/her shares, the sale must take place with one of the other existing shareholders, since no sale of shares can take place.
A closely held corporation is a private corporation, but a private corporation may or may not be closely held. In a closely held corporation, the management of the business may overlap with the primary shareholders.