When we refer to shares, we are normally talking about ordinary shares. There are however a number of different type of shares, with some of these being -

Ordinary Share - When purchasing an ordinary share, you own a share of the company. This entitles you to receive profits from the operations of the company in the form of dividends. At the annual general meeting (also referred to as an AGM), you also have voting rights.

Preferential Shares - A preference share is different to an ordinary share in that it gets preference, hence the name. Preference share holders receive dividends before dividends on ordinary shares are announced. If the company is wound up, preference share holders rank above ordinary share holders in the distribution of assets. Preference shares can often have a fixed dividend rate.

Contributing Shares - A contributing share is one that is not fully paid for and requires the holder to contribute payments at a future date.

Bonus Issue - This is a free issue of shares to the share holders based on the number of shares already owned.
Rights Issue - A rights issue can be granted to share holders to buy shares in the company, typically at a value below market price.