Both change the appearance of a webpage based on the browser environment. However, responsive sites respond to the size of the browser at ANY given point; adaptive sites adapt to the size of the browser at SPECIFIC points.
Think of the difference between smooth and snap design. Responsive layouts fluidly adjust, adaptive layouts snap into place at certain breakpoints. Adaptive requires creating several distinct layouts for different screen sizes, which can result is slower load times because the site has to load all of your layouts and then decide which one to use.