A stock and a share are essentially one and the same. They both represent a part of the capital of a joint stock company. In India it was always called shares whereas in the US they have been referred to as stocks. They essentially mean the same thing.
The stock market trades equity shares of various listed companies. In addition, the markets also trade other instruments like index futures, index options, stock futures, stock options, VIX futures etc. Both equity and derivative products are traded in stock markets.
There are various sources for finding stock related information like the newspaper, websites, company annual reports etc. Brokerage houses like Tradebulls also provide a plethora of rich stock market content and analytics on the website itself.