Agree - I think there is a big difference, in case this helps the terminology tips your hand - "remote-friendly" is a meaningless term in my experience.
Remote-first or Distributed are the "get on a plane to smell each other" terms of a truly remote team:
http://blog.davidtate.org/2016/12/remote-work-terminology/
Remote work - "Well, I live in [location on the other side of the world], so let me know when you have the airfare settled!"
Work outside of the office - "Okay, see you at [time later today]."
A lot of American companies allow you to "work outside of the office" but I think a lot of managers would not react too kindly to their people randomly being halfway across the country without being told.