git diff between two different files

Specify the paths explicitly:

git diff HEAD:full/path/to/foo full/path/to/bar

Check out the --find-renames option in the git-diff docs.

Credit: twaggs.

I believe using --no-index is what you're looking for:

git diff [<options>] --no-index [--] <path> <path>

as mentioned in the git manual:

This form is to compare the given two paths on the filesystem. You can omit the --no-index option when running the command in a working tree controlled by Git and at least one of the paths points outside the working tree, or when running the command outside a working tree controlled by Git.