Mobile web site is a website that specifically built for mobile phones. (all templates, content, graphics etc)
Responsive web site is the regular web site that you view on PC/Laptops and optimized for mobile browsers. Here if the visitor uses a regular browser, the site will display normal. If the visitor is using mobile browser, the site will be viewed with different templates.
NOTE: You need some backend code on your web site that detects mobile browsers and redirect users to mobile version of regular site.
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