I remember going through the MBTI manual, and seeing clearly that MBTI sees IPs and EJs as the "rational" types and IJs and EPs as the "irrational" ones. Also, I remember reading that the Myers/Briggs team came up with the J/P distinction as something they felt was more observable than rationality/irrationality. It seems pretty clear from that that in MBTI theory, rationality/irrationality refers to a different distinction than J/P, and different from the way rationality/irrationality is described in Socionics.
Well, okay ... maybe you are right about that. But the words "rationality" and "irrationality" have no clear function in MBTI, if it is not used as a way of referring to J and P types. And both models describe the actual behaviors of J and P types in very similar ways. An MBTI practitioner looking at an INTp would could call that person a rational type, because he or she is looking at an INTP.

But actually, many people in Socionics tend to define and similarly to the way they're viewed in MBTI, which is maybe why they think you're INTj.
Yes, and that is why we should focus on the types -- not those faulty and misleading descriptions of the functions. (How many times have I said that by now? But no one is willing to listen anyway ... or they are to lazy to try to understand what it means ...)