Having been a subscriber to Nintendo Force since near the first issue, I can give you a better answer :P
Once the announcement that Nintendo Power was ending came out, a group of fans got together to build what is now known as Nintendo Force. It has Matthew Taranto(sp?) from Brawl in the Family as one of the artists and reviewers, yes. They consider themselves as a spiritual successor to Nintendo Power, and iirc, they have said a few times that Nintendo knows about them...to the point where they actually had to change their name.
The first issue has "Nintendo Force" written on the side, but no other issue since has that, instead just "NF Magazine". Nintendo asked that they remove "Nintendo" from their name, as the magazine was not affiliated with them back then. "NF" no longer stands for anything, according to Lucas M. Thomas the founder, but they still call themselves Nintendo Force because that's how it started.
That said, I'm unsure where Nintendo stands on them now. They have sent NF free copies of games, allows them to post videos about them on NF's YouTube channel, and let them continue their Nintendo-focused work. At this point, it's kind of confusing what the relationship is between NF and Nintendo.