Stocks are generally classified according to their difference in cap, market price, dividend, type of industry, rules etc.
Ordinary: also known as common shares. Dividends are paid according to a certain profit from the company's turn over. Owners have more responsibilities in that they are the last to get anything when the company folds up and shares its assets. Apart from these all owners of these type of equities have equal voting right and dividends with respect to each individual unit of share.
Prefered: This is the type on which a fixed dividend is guaranteed before payment is made to other shareholders. The holder of this type of shares has a slightly better advantage of recovering some money in a case of liquidation. Usually except otherwise stated they don't have voting rights.
Convertible prefered: This gives the holder the option or opportunity to change his or her shares to ordinary/common shares at a pre-fixed price and date.