To expound upon this, temperament theory is one framework, and MBTI is another. They are based on different sets of factors, and thus are not always symmetrically mapped to one other.
You see in the link the name Kretschmer. He had what he called "four character styles". That's who Keirsey derived the groups directly from, and Kretschmer did not use MBTI dichotomies, but Keirsey matched his primary division (cyclothymes and schizothymes) to MBTI's S/N. Actually, Kretschmer's groups are traceable to Kant, and originally, Plato, who had his "four types of men", which Keirsey's familiar temperament names were taken from, and divided between "observant vs imaginative", which is obviously the first 'germ' of S/N.
The thing one has to understand about Keirsey's theory is that the
four temperaments themselves are the primary or fundamental categories, not the dichotomies, 16types, or any other factors, which only serve as making for "variants" (and as already mentioned, he rejected the functions). So to him, it didn't matter how exactly they mapped to the types; they were their own standalone units. (And you can really see this in his last two books, where he deprecates all the MBTI concepts).
However, he saw the same four groups in the theory of the other guy mentioned, Spränger, who had a factor called "social vs political". However, this factor did not map to any of the MBTI factors, so he had to create a new one of his own, called "cooperative vs pragmatic". Basically, this would end up connecting to J/P for S's and T/F for N's. That's why his theory maps onto S/N, but alternates between T/F and J/P.
The opposite groups, which have been called "mirror temperaments", do figure, in an even more loose way, onto the other four temperament grouping, the
Interaction Styles. Keirsey had divided the temperaments with a new factor called role-informative/directive, which was like the opposite of cooperative/pragmatic. S's now factored with T/F and N's with J/P. He had the eight last-three-letter groups using this, but when you add the original, classic "social"-temperament factor of I/E to this, you get four "social" groups even closer resembling the ancient four temperaments (of Galen and Hippocrates), but now even more complicated, as each Interaction Style is defined by an E/I + two separate S/N+T/F/J/P combinations (EST/ENJ, etc).
As you can see in the link Berens had further added another factor to Keirsey's temperaments, called "Structure vs motive". Classic temperament was originally I/E (expressiveness, or response delay) plus something called "people vs task focus" (responsiveness or response sustain).
Both Keirsey's temperaments and the Interaction Styles have this matrix, but one is covering social skills and the other is covering what are called "conative" skills (leadership, taking action).
So there are
two areas of temperament in each type. I/E is social expressiveness, and cooperative/pragmatic is leadership expressiveness. Informing/directing is social responsiveness, and structure/motive is leadership responsiveness.
While not totally symmetrical, there is a partial symmetry, in that F and P will across the board be generally more "people-focused" (whether socially, leadership-wise, or both when F and P are together), and T and J more "task focused". So TJ's end up as the most directive, FP's the least so, and TP and FJ inbetween. This explains why TP's and FJ's, especially on the N side, often have problems with J/P and especially T/F, as we expect T's to be more dry or serious, and F's to be more soft and accepting, but for the N's it can seem to be the opposite depending on J/P.