Boost Converter Design Formulas
I followed that Application note from TI once, back in 3rd semester, worked like a charm.

Can I use the App note formulas to design my boost converter inductor?


No I would not mix and match two different manufactors design notes.

Why are there different formulas for the same boost converter topology?


Many ways leads to Rome :) Sorry for the vague answer, I'm not entirely sure.
But I'm fairly confident the result should be the same if its the EXACT same topology.