There is an enormous difference between these two notions! Implied volatility is defined , for instance, with respect to the standard Black-Scholes model: given the interest-rate r, and the price of the stock you easily compute sigma, and that number is then called the implied volatility. You need this number in order to hedge , for instance, your options. Recall, that the BS-model is NOT used to price options, but to hedge options, Related notions : volatility surface, and an important name is that of Dupire.
I made a mistake ; given the stock price and the interest rate r and, say, the price of a european or american put option, you easily calculate sigma, the implied volatility, and with the help of this sigma you are able to hedge the option , and that is for an option trader very important. You do not use the implied volatility to price a vanilla option, the price is a result of the market.