Adaptive and Responsive web designs are ways of making your site fit any mobile device.
Responsive – fluidly change and respond to fit any screen or device size.
Adaptive – will change to fit a predetermined set of screen and device sizes.
“So, if you really want to pay attention to the mobile user experience and serve contextually relevant content to better serve your user and your business, yes, dynamic serving through RESS or adaptive Web design (or mobile URLs) is better for SEO than responsive Web design. There are still workarounds for both, however, so if you can make responsive Web design work well for your users and your business (which isn’t easy, as I’ve said manytimesbefore), it’s better to do that than adaptive Web design or RESS.”
–Bryson Meunier, Marketing Land Blog