In simple words,
Director is the person who takes the responsibility to run the business and manages the day to day business of the company. Generally are the managers or agents of the actual owners of the company who act in fiduciary (Trustworthy) position. Only Individual Persons can Become directors.
Shareholders are the owners of the company who invest their monies in the company. Shareholders get part in the profits of the company in the form of dividend. They aren't responsible for the day-to-day management of the company, but they do have voting rights with which they can affect the decisions of the company. Any Individual, company or other entity can become shareholder.