Did your web firm tell you that your site was "mobile-friendly", but now you find you need to update it to keep Google happy?
No, they weren't lying to you.
Until Google decided to use the term to mean something else, "mobile-friendly" was the term used by website people for a site that displayed accurately and the same on desktops, laptops, tablets, and smartphones, simply adjusting the size to fit the screens. We, and most good web firms, built all sites that way.
"Mobile-optimized" meant something much more advanced. The layout automatically reformatted depending on the device viewing the website. Until fairly recently, that meant a separate design and programming for each different sized device. In most cases, this proved cost-prohibitive.
Evolving technology has made it possible to program sites that respond to the size of the device. So many new "mobile optimized" websites are "responsive". Others show separate layouts that were created specifically for different devices.
Google changes the definition...
Google has taken the position that what we called "mobile-friendly" is no longer friendly enough, as the use of smartphones to access the Internet has skyrocketed. By their definition now, "mobile-friendly" now requires that the site be "mobile-optimized."