Adaptive web design (AWD) promotes the creation of multiple versions of a web page to better fit the user's device, as opposed to a single version that other web design techniques use. Adaptive web design encompasses a range of other strategies that can be combined with responsive web design.
"Mobile separate" is the same concept as "mobile first", except the design layout of AWD is to have a separate base mobile layout versus the single design layout of RWD.
The Link below is a good explanation of the two concepts.
My view is, if you ever want to aspire to having a fast experience for your mobile customers, adaptive is the only way. To achieve the one second load goal set by Google it will be by only taking stuff away and responsive simply doesn't help this, no matter how awesome the design.
One of the greatest advantages of AWD over RWD is the ability to segment mobile traffic and deliver device specific experiences.
My advice is to design a site which works for the user. To me a site that is convenient for the designer / developer to construct without the end user is only a big short cut.
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