Both MBTI and Socionics are Correct?

[EyeSeeCold]

I'm not entirely sure Jungian functions and dichotomies match, actually.

I agree. MBTI functions have kind of been meshed together, most likely because of introverts.

Now, I would suggest myself that for both systems to be more precise they need some modification. Particularly Socionics -- it is much too complicated. For every type trait defined by Socionics to be true of every type all the time you need to cut down some.

Maybe it is complicated, but the bulk of material leaves a lot of potential.

why do either have to be "correct"?

Eh I forget not everyone thinks like me. By correct, I mean neither of the systems are wrong, or useless based on subtle differences.