A responsive website shows content based on the available browser space. If you open a responsive site on the desktop and then change the size of the browser window, the content will move dynamically to arrange itself (at least in theory) optimally for the browser window. On mobile phones, this process is automatic; the site checks for the available space and then presents itself in the ideal arrangement.
Adaptive design has multiple fixed layout sizes. When the site detects the available space, it selects the layout most appropriate for the screen. So, when you open a browser on the desktop, the site chooses the best layout for that desktop screen; resizing the browser has no impact on the design.