A responsive website is a website that adapts to the device it is being viewed on. For example, if you view a site on a laptop and then view the site on a mobile, you should have equally good experiences of that website but not the same experience. On the mobile, the website may have a slightly different design and content may have moved to make it easier to navigate and view utilising the controls available on a mobile device.
A mobile friendly website will give you the same user experience when you view it on a mobile device as well as a large screen. In contrast to the responsive website, there will not be a specific design for mobile usage, but the whole site will be designed and built in such a way that all features are available and equally usable on all size device