First at all according to google: You Can Have Completely Different Content On Mobile Says Google.

Google’s Gary Illyes confirmed what had been known before — for many of the factors and ranking criteria around mobile, Google looks at the desktop version of a web page instead of the mobile version. E. g. when you have a page about cats on the desktop and you change the content on mobile to dogs, Google will rank the mobile version as if the page was about cats.

He also explained  that it doesn’t mean that Google won’t be able to take action on webmasters who take this route. Google can apply manual actions and penalties when needed, but they have not needed to yet. This was one reason for Google to build a separate mobile index and not share the desktop index with the mobile index. Illyes said Google has been experimenting with this, but he does not know if Google will ever  end up going with a separate mobile index. There are pros and cons to both methods.

A mobile site is seen in the mobile search results as the page from the desktop crawl:

Additionally, Google added  the mobile-only factors: