To me, Fi and Ti are very similar. The way they work is essentially the same. The difference is what building blocks Fi or Ti uses to come to conclusions. Ti will draw from what it feels are objective,'logical/factual' whereas Fi doesn't pretend to objective (well...most of the time) and is guided by what is 'right' by objective logic. Fi draws the building blocks from principles, feelings, etc. and is guided by what is 'right' by subjective logic.
The thing is, both Ti and Fi are drawing from a personal internal inventory. Decisions based on Ti are not necessarily more "correct" than those based on Fi. The Ti process is still personal to the user, so the person may choose wrong or inaccurate building blocks. Just look at a group of NTs arguing amongst themselves about what the best way to XYZ is.
Personally, I feel I often use combinations of Fi or Ti. For me, they seem to operate very similarly at least.