Mobile Friendly Website
Basically, a mobile friendly website will look good on mobile devices. But might have glitches and be harder to navigate when viewed on devices with a higher resolution.
While a responsive website is a website that allows your website to adapt to the size of any screen it is being viewed on.
So, it could be viewed on say, a desktop, phone, or a tablet etc and users won’t ‘notice any difference’ in your site’s general appearance on their screen.