(a) That's right. A proprietary company must have at least one 'member'. 'Members' are persons who own a share in the company and are also referred to as 'shareholders'. Collectively, the shareholders own the company, and they also have the right to participate in some of the decision-making that affects the company. But generally speaking, the shareholders are not the people who manage the day-to-day business of the company. Shareholders are investors who contribute assets to provide the company with the capital it needs to start and run a business. Shareholders hope to receive a share of the profits made by the company.
The day-to-day management of a company is carried out by one or more persons who are appointed by the members as 'directors'. Proprietary companies must have at least one director: public companies must have at least three. In a small 'one-person' company, the same person will be the sole shareholder and the director. If there is more than one director, they are referred to collectively as a 'board of directors'. A board of directors may manage the company jointly, or they may appoint one director as the 'managing director' to run the business and report back to the board.
In addition to directors, a public company must have a secretary who is responsible for keeping the company records, giving notice of meetings, signing documents and ensuring compliance with all legal requirements and regulations. Since 2000, proprietary companies may appoint a secretary but are not obliged to do so. In a small 'one-person' company, the director will carry out the duties of a company secretary.
A company can also employ people to work for the company. Employees do not automatically have the power to alter the legal rights and duties of the company, but individual employees might be vested with an agency power, so that they can represent the company.