Responsive and adaptive web design are closely related, and often transposed as one in the same. Responsive generally means to react quickly and positively to any change, while adaptive means to be easily modified for a new purpose or situation, such as change. With responsive design websites continually and fluidly change based on different factors, such as viewport width, while adaptive websites are built to a groups of preset factors. A combination of the two is ideal, providing the perfect formula for functional websites. Which term is used specifically doesn’t make a huge difference.
Mobile, on the other hand, generally means to build a separate website commonly on a new domain solely for mobile users. While this does occasionally have it’s place, it normally isn’t a great idea. Mobile websites can be extremely light but they do come with the dependencies of a new code base and browser sniffing, all of which can become an obstacle for both developers and users.
Currently the most popular technique lies within responsive web design, favoring design that dynamically adapts to different browser and device viewports, changing layout and content along the way. This solution has the benefits of being all three, responsive, adaptive, and mobile.