How can I copy files from a branch to another using git?

You can:

git checkout gh-pages
git checkout master foo
git commit -m 'Add file foo to gh-pages.'

If you want to compare all the diffs between 2 branches: you can use git difftool master gh-pages or git difftool <SHA1 of gh-pages> .

If you want to get diff for specific list of files follow this:

git diff master gh-pages -- path/to/file

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