Why does a photo copied in Photoshop from one window to another display with a different tone than the original, regardless of the duplication method?

​@SEVO  I agree with the others that this change youre seeing is likely a product of differing colour spaces for each image (document ) / window.

​as @dianer_macperson wrote, “this can be checked by looking at “edit>assign profile.” from the Photoshop menu and checking the current profile with each window selected in turn.

There is also an option at the image window bottom left to display the colour profile for that window. 

Ai helps with this “To display the current color profile for an open document in Adobe Photoshop, look at the status bar at the bottom of the document window.  If the profile name is not visible, click the small arrow next to the zoom level or document information to open a dropdown menu.  From this menu, select Document Profile to make the active color profile permanently visible in the status bar.”

I hope this helps

neil barstow colourmanagement - adobe forum volunteer,
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Be sure your color settings and profiles are the same for each document. 

edit>color settings

edit>assign (or convert to) profile.

How would you describe the different results? Is it a difference in size, contrast, colors, or something else?

For example, some common causes are the two documents having different ppi resolutions or different document color spaces.

Please set the Status Bar to »Document Profile« and post meaningful screenshots including all pertinent Panels (Toolbar, Layers, Channels, Options Bar, …).

What are the images’ Color Spaces? 

What are the Edit > Color Settings?