A stock is a general term used to describe the ownership certificates of any company. A share, on the other hand, refers to the stock certificate of a particular company. Holding a particular company's share makes you a shareholder.
There is also something called 'convertible preferred stock'. This is basically a preferred stock with an option of converting into a fixed number of common shares, usually any time after a predetermined date.
Shares can rise in value over time and you may be able to sell them for more than you bought them, with the difference in those prices known as your capital growth.
When a person owns stock in a company, the individual is called a shareholder and is eligible to claim part of the company’s residual assets and earnings (should the company ever have to dissolve). A shareholder may also be referred to as a stockholder.