Default noise texture node and default displacement node used as displacement in cycles on the right.
How do I get exactly the same result with geometry nodes on the left?
subtract 0.5 after noise texture it does the same thing with midlevel in displacement shader node
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Yeah. See, I would never have figured that out in 10 thousand hours of trying.
Ok. I officially give up on gometry nodes. I will happily sit in ignorance and wait a few years for the people who actually know what they are doing to produce more user friendly massive packs of node groups.
This is 700 words too short for me to get any understanding from 
don’t get intimidated. 1 step at a time. you don’t need to complicate stuff. It is almost the same here with this simple set up
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That’s the reason why in math ( as in any other area) there are special vocabulary / domain language which would tell you this in less words…
The texture doesn’t depend on the exact values of the positional coordinates but transforms them to a “bordered” box (bounded) within only values from 0.0 to 1.0.
So you first trial was already a good start… (i tried also a little and thought: there must be any transformation)…
Edit: Ohhh… i’m mixing this with you ither thread…
… well the thing about math is… it applies here also 
I would have been here another few hours before got around to combining those particular nodes in that way. It’s just not a good use of time.
And my results are quite different:
aww that is true, i think I have put subdivision modifier after geonodes accidentally so they looked alike. Then Higgas method is way to go. Sorry if I confused you.