They are interchangeable. "Stock" is characteristically used in North America, and "share" is characteristically used in the United Kingdom and the commonwealth, but the mean the same thing: part of the ownership of the company's equity. The reasons are historical - all companies used to be called "joint stock companies" (merchants pooled their money to buy trading stock, and then ship it together to some far flung destination). About this time in history some Americans got antsy about taxes, tossed some tea in the water in Boston, fired a few shots at King George's finest, and went their own way on legal matters. They continued to refer to ownership of companies (which they started to call "corporations") as stock, whereas in Britain they started to use the term "share" when merchants started to own the company, rather that the company's trading stock. Some jurisdictions refer to them as "quotas", and they are referred to as a percentage of the whole, rather than a fixed number which is the usual case with stocks/shares.
