Kind of, you could say it I guess.
Video games are all obviously made by someone, and the groups that make them are called developers. Some examples are Nintendo, Game Freak, Microsoft, Retro Studios, Sanzaru Studios, Namco Bandai, and countless others. The point is that different groups make the different games.
Sony, Microsoft, and Nintendo are special in that they are the groups that not only develop games, but also develop major systems. (The Ps3, 360, and Wii, not to mention all the handhelds, and the new stuff they have coming up)
Because they can command so much more potential, the developers that also make the consoles will almost always enlist the help of developers to make games for them. Nintendo is their own developer, but they can enlist groups to make games for their franchises, helping sales for the game, the consoles, and for the developer, helping everyone.
That's what game freak is: a partner, rather than an offshoot. Currently, they pretty much work exclusively since pokemon is the most famous series they're known for, but that doesn't mean that they are necessarily bound to nintendo and "Related" as it would imply.