Responsive design means that the site’s desktop version or landing page will adjust to mobile screens. The difference from mobile-first is that the desktop is still put in the first place with this approach.
In a responsive design, the site layout adjusts to the screen’s width a person is viewing the page on. Even if the browser window changes by one pixel, the page will automatically adapt to the new dimensions to avoid wasting time creating a mobile version of the site. At the same time, it will not be superfluous to make sure that all the elements look good on different devices.
The Mobile-First strategy is built from the opposite: first, the site is made for smartphones and then finalized for desktops. There is no feeling that the mobile version is inferior in this case.