Graceful Degradation is the practice of building a website or web application so it provides a good level of user experience on modern web browsers. However, on older browsers, the website will degrade slowly. It may not be as as visually appealing but the basic functionality will still be there.
Progressive Enhancement on the other hand provides a base level of user experience for most browsers. More advanced functionality may be viewed if a browser supports it. So it enhances the experience for browsers that support it, but has no impact on browsers that do not.