As for me there is difference between desktop and mobile SEO. There are nuances and differences in optimizing mobile sites that don't apply to desktop sites, and some that apply more to mobile sites than they do to desktop sites. Also there are different standards for mobile sites because of the different user experience.
First thing is that not all mobile users are searching with keywords. With Voice Search, for example, a mobile user doesn't have to go to the Google home screen and type in a query anymore and that can change how their intent is conveyed. And, sometimes the mobile context is going to change the frequency or type of their needs.
Secondly, a mobile searcher (compared to a desktop searcher) is highly engaged, but is less interested in scrolling than a desktop searcher.