There are a number of important issues at work, which I love to ramble about, as I love precise cross-system comparison.
The biggest difference between socionics and the MBTI-functions theory lies in their respective definitions of e/i. In the latter, it's basically going with Jung: it's sort of saying it's an "inner vs outer world" distinction, which in practice to Jung basically meant mind vs external to mind (think in terms of philosophy's mind-body dualism). Socionics has a different twist on this -- those familiar with some philosophy know of arguments that say things to the effect of relations like causality are imposed by the mind, and not "present" in the external world. I think this intuitive idea is the starting point for saying e/i is about the "objects vs relations" dichotomy...it means there's both a parallel to Jung's original intent and a difference in exactly how that intent is implemented. Socionics uses an analogy with physics, where relations are construed in terms of fields in physics (think of the idea in modern physics that fields can be thought of as the fundamental subject of physics, rather than particles -- fields seem in some sense more mathematically defined and indirect, but they're viewed as very "real").
What this in practice means is that we no longer think of introverted information elements (IE) in socionics as about the "self" -- at least even if some socionics sources try to continue on with that Jungian parallel, they're probably not the best interpretation.
So think of the two dimensions of logic: Te/Ti are factual vs structural logic. Structural logic is basically the purest expression of logical relations.
Personally, this is one area where I plainly feel the socionics interpretation is better. Why? Because the truth is the inner/outer dichotomy doesn't seem to work equally well with N, F, S, T -- in particular, N is simply more "inner" than S -- and this is a well-known fact for those very familiar with Jung, that he somewhat insufficiently distinguished his own intuition-sensation dichotomy from his introvert-extravert one: BOTH wound up some kind of "mind/senses" dichotomy. And in fact, this may be what led him to "mistype" himself as a thinking-sensation type instead of a thinking-intuitive (which he changed his self-diagnosis to in later years).
The major change for INFp/INFj vs INFP/INFJ is going to be the definitions of Fe and Fi. Fe in socionics is ethics of emotions, Fi is ethics of relations....it is very conceivable for Fi ethics of relations to not be "more oriented inward/to the self' than "oriented outwards" !
I would say the way to understand this is that Te being factual logic and Ti being structural logic (thus responsible for sort of defining the framework under which one can derive facts) is analogous to socionics' Fe/Fi -- how you relate to something is extremely "defining" of how you can and cannot derive a value judgment from it. The ethics of emotional reactions is more akin to the "factual" side of ethical processing: that is, there's a school in philosophy that says emotions, while not ethical themselves necessarily, betray certain attitudes which ARE ethical (i.e. have value content) -- and that someone has such reactions is something akin to a fact rather than a framework for ethical processing.
There is still some parallel to the Jungian/MBTI functions version of Fe, in that ethics of emotions deals with the more outwardly expressed form of F, but that doesn't change that there are some differences in organization. In particular, Fi need not be perceiving how one *oneself* relates to something, which may be closer to the MBTI concept, but rather may be perceiving how two people external to oneself are ethically related. So the "frameworks vs facts" view seems more universally applicable here. I tend to think Jung's typing of Kant as Ti-dom carries over here.
I tried to keep it "short," but I can go on a lot about many other issues (such as how Ni and Ne differ), but these are some of the ones that jump at me.
I'm very critical of socionics mainstream stuff, like VI, but I think the core ideas and organization are very good, and I decided this after a long time studying Jung, the MBTI, and so on. I'm happy to discuss why that's so. To be frank though, my reasons for thinking they're "good" are a little more related to how well they organize Jungian-related ideas, which I find fascinating, than in believing they're necessarily the most empirical way to describe people.
Added--one other really important difference is that there isn't quite as uniform an order to the IE in socionics...in the sense that an NeTi type is no longer "S-inferior" but rather more conditional: Se is considered stronger than Si, and Fe more than Fi.
The gist is socionics seems to respect the irrational-rational dichotomy more equally, in that a ILE doesn't JUST have Si-suggestive, it also has Fi polr.
The idea behind this is that Jung originally ascribed 2 qualities to the inferior function. One is that it is a point of suggestibility/where the individual operates without much ego and can exprience great spiritual bliss by tapping it, the other is that it's a point of high sensitivity. Socionics seems to say these 2 qualities don't tend to belong to the same IE. For my ILE, e.g., Fi and Si are treated differently.
Now if someone feels any of these designations are arbitrary, I'm the first to say they are not empirical that is, they're not derived from direct observation of how things tend to occur in nature. However, I do think on a philosophical level one can argue why these organizations are meaningful.
