Total Commander

If I synchronize folders and need to move the differences to another folder or compress, I would be able to move the filtered files from the left or right list to the standard panel, as in the case of a search.

No need for that, it works just within "Synchonze Dirs"!
Right after you had compared the files of location A with location B you just have to modify the destination path entry on top of the list to your new destination and press "Synchonize" ... easy go