도록 vs. 기(를) 위해 ...how different?

Question

Lately, this has been coming up quite a bit in my Korean studies. In the case of meaning something like "in order to" are these fundamentally the same? I have been getting mixed (seemingly context-dependent) answers from natives about this.. Here are two example cases, for a starting point: 긴장을 풀기(를) 위해 뭘 해요? 긴장을 풀도록 뭘 해요? and 지리산을 올라가도록 적어도 2일이 필요하다. 지리산을 올라가기 위해 적어도 2일이 필요하다. thanks for any help.

Answer 1

도록 and 기 위해 are not the same.

도록 translates into “ to the point “ while 기 위해 does “ in order to”

Answer 2

1. ~하기 위해 : for, to verb, in order to verve, in order that
2. ~하도록, ~할 수 있도록 : so that ~