I am afraid I don’t understand the problem.
Are the two images two Layers in the same file already or do you need to place them yet?
Do you need to duplicate the image Layer (cmd-J) first and apply the color correction to it or …?
You will need to increase the size of your canvas so that both images will fit side by side (use menu Image >Canvas Size)
Then position each layer so you can see both.
If the top layer does not have transparency - select the wanted part with the rectangular marquee tool - and go menu Layer>Layer Mask >Reveal Selection).
That will add a mask to the upper layer allowing the lower layer to show through ( layer mask shows the layer where the mask is white and shows the layer(s) below where the mask is black)
Thank you Dave ! So I understand that I always have to use layer masks in order to do things like that ?
You could also delete the excess data but that is often a bad idea.
Ok, thanks to both of you
As cpfaffenbilcher said - it is best to use masking wherever you can. A mask can be undone and altered later (even years later if you save the document in a format that supports layers (such as psd). Whereas cutting out areas is a destructive step which can only be undone by stepping back through history and that history is lost once you save the document.