Essentially, responsive and adaptive design both aim to solve the same kind of problem: how user experience across different devices (with different viewport sizes, resolutions, usage contexts, control mechanisms, etc.) can be optimized without having to create a separate site for each device supported. But they approach the problem in different ways, so it is worth getting this distinction clear.
- Responsive design works on the principle of flexibility--the idea that a base of media queries, flexible grids, and responsive images can be used to create a user experience that will flex and change based on platform/browser differences. For example, a single fluid design can flex to look decent across a variety of screen sizes, even before media queries come into play.
- Adaptive design is kind of like the modern definition of progressive enhancement, and it uses many of the same ideas. The main difference is in execution: Instead of a flexible set of designs that can respond to multiple variations in viewport size, etc., adaptive design tends to use a predefined set of viewport sizes and other characteristics, detecting devices/features and then serving the appropriate feature/layout set to give the device/browser the best experience that it can handle.