Responsive Web Design, which is built on the principals of Graceful Degradation.
Adaptive Web Design is built on the principals of Progressive Enhancement.
Graceful Degradation is when you build your site for modern browsers, then find solutions to make the experience passable for people using Internet Explorer or Mobile Browsers.
Progressive Enhancement starts with a solid base, designing as for the lowest common denominator, then adding enhancements for a better experience for the more fortunate visitors.
This is a somewhat of a watered down analysis. But essentially, it’s a difference of approaches. Who is your audience? are you targeting, mostly, people who use modern browsers and you just want to make sure it just works OK elsewhere? There’s nothing wrong with Progressive Enhancement… when it’s intentional. Personally, I’m a fan of inclusive thinking.