according to a grammar site
Try + -ing means that you are trying something as an experiment, especially as a possible solution to a problem, to see if it works or not.
Try + to + infinitive means that something is difficult but you are making an effort to do it.
But in some posts like a StackExchange post
I can't find mention of a degree of effort. In Korea, I've been taught to strictly distinguish two of them(by what "a grammar site" says), so it's confusing to me that they don't talk about a degree of effort.