What you describe is normal short selling. The recent innovation that has turned many people against shorts is naked short selling.
In this case you sell stock even though you don't have it. You can do this because the market rules gives you a certain amount of time to actually turn over the stock. This time window, for historical reasons back when the exchange involved actual paper stock, is actually several days. Normal sales are all electronic now and usually done within fractions of seconds.
This form of short selling lets the short sellers drive the price of a stock down. By pumping their non-existent stock sales into the market they increase supply and reduce demand. This pushes the price down, making it possible for them to buy at a lower price and make money.
My opinion is that short selling is a valid, if risky, form of investment. Naked short selling is a form of market manipulation.
Jay