Mobile-friendly means a site built for cell phones. Responsive means a site built for all devices.
Google, who has the lion share of the search market,
is launching an algorithm to favor sites that are “mobile-friendly.” This means that people who use Google to search on their smartphone may not find many of their favorite sites at the top of the rankings. Sites that haven’t updated could find themselves ranked way lower, which in turn could mean a huge loss of business.
Google is doing this because it wants consumers to “find content that’s not only relevant and timely, but also easy to read and interact with on smaller mobile screens,” Google said in a statement.
– USA Today, 4/21/15
This is even truer today than when this was written. Those of us in the Web development field have known about this for a long time and have been encouraging clients to go responsive with very old sites which were not built as mobile-friendly.