I think "pure" mbti is divided on whether the model should be (using ESFP as an example) Se Fi, Se Fi Te Ni, or Se Fi Ti Ni, basically saying that the rest of the functions don't exist (read this a long time ago and I have no idea where).

There are a few mbti-related models from people or groups who don't belong to the mbti "core". The one most people seem to have heard of and use is the Se Fi Te Ni / Si Fe Ti Ne, where the functions before the / are supposed to feel "normal" to use, and the ones after would make you feel awkward and "not yourself". Si and Fe would often be quite strong and Ti and Ne would be the weakest according to the model.

If you look at the roles the different functions are supposed to fulfill in that last model and in the socionics model a, they actually seem remarkable similar.

I don't see the models as being the main problem with understanding between the systems, but the fact that mbti tries work all its theory around the supposition that you will only use, display, and interact with your extraverted function(s?) in the "external" world and that you will only use your introverted functions in the internal world. (Which is where the j/p confusion comes from.) It creates paradoxes and strange special cases and confuses the theory.