I think these are similar things that have to with shares of a particular company. The difference might've due to economical and financial terms. Share is a portion of a particular company purchased but and external body while stock is the trading of the collection of shares.The key difference between stock and shares is that stock is the broad term which is used more generally to represent the ownership of a person in one or more than one companies in the market, whereas, the term share in comparatively a narrow term which is used to represent the ownership of a person in a particular single company in the market.