The terms stock and shares are used separately and often together and the way these two terms are used is often confusing to those who don't deal in stocks. However, don't let these terms confuse you as basically the two words often mean the same thing, but are used to connote slightly different meanings. By looking at these two terms when they are used together and separately you will get a clearer understanding of what these terms mean and the very slightly difference between them.
When someone refers to stock shares this simply means that they have paid money in exchange for owning a piece of a company. How much of a company one owns depends on how many shares of stock he has purchased. The term stock actually means the paper that you get saying you own part of the company. Shares in this case means how many small pieces of the company you own.
When people simply use the term stock or stocks they are referring to owning a piece of one or more companies. While share used alone usually refers to owning stock in a specific company. For instance if you own stock in a toy company, an internet company, and a food company you might say "Some of my stocks are doing extremely well." However, if you are referring to just your stock in the food company you might say "My shares in General Mills is worth more now than when I purchased them five years ago."
In both cases you are referring to the same general thing, the portion you own in a company or companies. One is used as a general term the other as a more specific term. However, in recent years these terms have become almost interchangeable and therefore you should not worry too much over which word is used or allow yourself to become too confused over these two terms.