If MBTI and Socionics had such a succinct match-up, then why have the theories not merged yet? They both have the Jungian system in common, but MBTI used that as its basis while Augusta adopted it later as it seemed to be a useful vessel for communicating her already-formed conclusions. The two systems have some weak correlations, but only weak ones. The IMs/functions are entirely different breeds between the two.

Although there's no direct correlation, MBTI J/P seems to correlate more with static/dynamic than rational/irrational. It's a difference on what each system thinks to be important for understanding a person. MBTI places more focus on what a person's strongest extraverted function is, regardless of it's position in MBTI functional ordering. (which isn't anywhere near as rigid as in Socionics; you can hear "My Te is stronger than my Ti" statements in casual MBTI discussions, which aren't commonplace around here)

Just as certain types tend to often have a certain "range" of E-types, the same works for MBTI. Some pairings occur more than others, but there isn't a smooth dichotomy-for-dichotomy comparison between the two.