Ti/Fe axis would be looking at values objectively (what the "group" agrees to be socially acceptable/fair/right), and using logic to rationalize these values within oneself.
Fi/Te axis would be looking at values subjectively (what the individual feels to be socially acceptable/fair/right), and using logic to project these values into the world.
Te structures it's environment to reflect its inner values (Fi).
Ti reasons itself into alignment with what it sees as valuable within its group (Fe). Group could be anything from spouse, friends, culture, or even religion.
Im also looking at the axis in relation to my most prominent function, which is introverted, so, my descriptions may be putting more emphasis on the extroverted judging functions since they would be my auxiliary. They also may be completely wrong Lol. Based on the information I've consumed and my actual observations of people so far, these do seem to be true though.
Ive also had a complete turnaround since this post due to something I realized. At the time of this post my interpretation of the Ti/Fe axis was a bit shakey. I've actually never been to prominent of a Fe user myself, I was just mistaken my conforming/people pleasing tendacies for that (probably a weak Te more than anything). I still however feel Functions can be developed with conscious effort though. I don't buy the whole "your personality type can't change" thing.
Sorry for the delayed response.
Good response. I didn't want to lecture you if you already understood things.
Fe/Ti users can have strong personal values/ethics and not conform to the group. Fi/Te users can be conformist.
For me, the fundamental difference is that Fe users are more connected to the external emotional environment, while Fi users are more contacted to their own internal emotional environment.
I have written somewhere here about type development. Each function has two aspects, and we merely have a preference for one and the other one is subconscious.
We never really get too strong in our inferior function, no matter how mature we get, but, if we work on our shadow, we can have some use of the opposite aspect of our dominant function.
No one will switch axis, but one could make greater use of the other. A Te dom could start developing a form of Ti and become start creating their logic more, rather than use established external tools....
People's type does not change, but their understanding of themselves changes. One type theorist I like argues that it goes during young adulthood, the inferior function asserts itself and there is a rough patch until it gets integrated into the dominant function (sometime before 25, when the brain is fully developed).
Self-perception is a huge factor in typing mistakes. A person can see themselves as introverted and flexible and struggling to make friends, but really be a very outgoing ENFJ just failing to properly see themselves--- that was me, and I tested consistently as a ISTP, which, of course, uses the same functions as a ENFJ, just upside down.
I am not a STP at all and my education and career path would be near impossible for a true ISTP, though I have enjoyed STP style activities at occasion.