MBTT is the Myers-Briggs Type Theory, which is the theory that tries to explain why the real types are what they are. MBTT and Socioncs describe the exact same groups of people (identified by the four dichotomies), but their theoretical explanations for them are different. The two theories agree on what the real types are in their typical behaviours and attitudes, what they look like, etc., and they agree on how to group them according to temperaments, test results, dichotomies, and so on. But MBTT has confused Jung's functions for the introverted types, which has resulted in the well-known mess that is the major cause of all mistypings on this forum and elsewhere.
If we look at how Jung described the types and compare that with how MBTT and Socionics describe the types, we find that the essence of Introverted Thinking in Jung's sense is also the essence of -- but it is not the essence of Ti in MBTT. Ti in MBTT is essentially much more like Extraverted Thinking in Jung's sense, and in socionic terms Ti (in MBTT) is some sort of mixture of and (with perhaps some traits of ), and it is very important to notice that INTPs in MBTT are always described as having a focus on the external world, on objectivity, objective truth and knowledge, etc., which is clearly in Socionics. The INTJs and the INTjs (LIIs) on the other hand, are recognized as "systems thinkers" in both models, they have a focus on implementing their subjective systems, ideas, etc. instead of seeking the objective truth, and that is the essence of and Introverted thinking in Jung's sense.
We also find, when we compare the theories with reality, that INTjs (LIIs) always exhibit J behaviour and attitudes, that all of them seem to be early birds, that many of them are relativists of some sort, that many of them criticize typical notions like the concept of an objective reality, the concept of truth as correspondence with reality, etc. That is in the nature of , but it is certainly not the nature of being an INTP in MBTT or an ILI in Socionics. And we find that INTps (ILIs) always exhibit P behaviour and attitudes, that all of them seem to be night owls, that they tend to be objectivists and especially empiricists to a much greater extent than INTjs, and they tend to accept (and more important, in contrast to the INTjs, the INTps understand the concept truth correctly as it should be understood, as correspondence with reality).
MBTI is the Myers-Briggs Type Indicator, which is nothing but a typing intstrument, and in that respect it is no different from socionic tests, even though MBTI tests tend to be more accurate than most socionic test and can therefore be recommended as one of several means to determine a person's socionic type.