They are both used but often in different ways. You might say "that's the way to do something" and "that person has their own way of doing things"

They are both correct. Michael Swan's Practical English Usage ( the British grammarian's 'bible' ) says: 'After way (meaning 'method/manner') we can use an infinitive structure or of … ing. There is no important difference between the two structures. There is no way to prove / of proving that he was stealing.' So 'no important difference'. But I would agree with Ashley's suggestion that the infinitive version may imply that it is perhaps the only way, whereas the 'of + ..ing' construction may imply that there are alternative ways. But the distinction is so subtle that it probably isn't worth worrying about.

Hi Camilo. I am not sure I understand the question; but I think you may be looking for a general term to describe "way"? Method is a word that may work for you.