They're both attempts to map out the psyche into 8 cognitive processes, however they use different descriptions and function orders for the types. The socionics function order and intertype relations are incorrect, and I am unsure how the model got as much information associated with it as it did. Socionics is quite mathematical, but when you're getting the math wrong all that really does is create a nice theoretical framework.
What you're referring to do with Ni for INTP is the difference in labelling the types based on their top two functions. MBTI uses P to mean that the introverted judgement and extroverted perception processes are involved in the top two, whereas socionics means that the top process is a perception process.
If you're wondering whether to learn more about it I would probably say don't bother, but if you do then keep in mind that you're dealing with very major inaccuracies. The correct order for the conscious processes of the INTP is Ti-Ne-Si-Fe, not Ti-Ne-Fi-Se, and the correct optimal pairing for Ti-Ne is Te-Ni, not Fe-Si.
Beyond this there's Reinin dichotomies, but I really doubt that the obscure divisions across types which are made from the on/off of other dichotomies really is valid. It's like there's all these dichotomies which probably do apply to types but not in the way that it's described by socionics. So it's an alright collection of possibilities relating to the psyche but it's nothing to pull definitive insights from.
I was interested in the subject for a while, but now I have no interest in it because of its glaring inaccuracies. Pod'lair incorporates the best aspects of the MBTI but goes far beyond it. In MBTI even there is no real way to determine someone's type, but Pod'lair details methodology of how to do so. But MBTI, or at least the collection of theories on typology that tend on the internet to be put under the MBTI heading, have a lot right in terms of the theory.
My favourite aspect at the moment of type dynamics is what may be termed the Peak Pathway, but I stumbled across it independently. What it means is that functions go around in a cycle, basically one after the other, in an order matching the full function order, which for INTP is Ti-Ne-Si-Fe--Te-Ni-Se-Fi--Ti-etc, so if you can determine your type you can see what order your functions move in, or conversely, if you can see what order your functions move in, you can determine your type (this is how I gained certainty over my type - I observed that I seemed to be using an Ni-Fe-Ti-Se function order in my posts).
So all these systems are an attempt to describe people according to 8 cognitive processes, and Jung was the first one to outline what he thought these processes basically were. The basic framework is something that modern approaches correlate with, but Jung was a pioneer, not the authority, so naturally there may be quite little of his work that remains in what we have now. Remember too that Jung wrote about much more than just the cognitive types, and so there is plenty about other aspects of the human condition in his work, such as archetypes, which are structure of the unconscious mind which operate behind the scenes in a kind of drama of the psyche and have their effects manifested in conscious thought and behaviour. It details how mythology relates to day to day functioning, and the process of individuation, of, alchemically speaking, turning lead to gold. So if your primary goal is to become the ultimate person you can be, the theory of types can give you a reference point as to what you should be doing on a psychological level, and more concrete in terms of your behaviour and interactions, and this can put you in a greater position of personal understanding and development. Theory is one thing, but ultimately you need a theory that will guide your everyday life and life-story, so you want a system which reflects accurate understanding or you'll flounder around when trying to understand it. The pieces will only come together if things are positioned in the right shape, so it is important to have the correct map if you're going to use a map to develop yourself.
So that's a brief rundown on my views of the subject, hopefully I half-answered your questions and provided you with more insight and things to muse over.
