A shareholder is purely a provider of share capital to a company. In other words, they are a part owner of the company. Their liability is limited to the capital they have put in. They have no responsibilities.
A director is appointed by the shareholders at an AGM to represent their interests in the company. They have very onerous responsibilities which are summarised [broken link removed].
In a large publicly quoted company such as CRH plc, there are thousands of shareholders and maybe a dozen directors.
In a small private "one man" company there are often two shareholders each of which is also a director.
"Executive" directors are full time employees of the company. "Non-executive" directors are not full-time employees. However, I don't think that there is any difference in their responsibilities as directors.