MBTT is a functional theory, and so is Socionics. Keirsey's, Spranger's, Groos's, and James's typologies are not based on functions. Keirsey describes the same 16 types as those in MBTT and Socionics, though, and all three (MBTT, Socionics, and Keirsey) define the 16 types in the four dimensions.

And all three also test people's types by using a testing method where they ask questions that are based on the four dimensions that define the types. The only reason people have got the incorrect idea that MBTT is not a functional theory and that it is all about the four dimensions is because the testing method (which of course does not define your type in any way) is so much in focus due to the industry that has been built around it.