Public Face Righteousness, Private Face Holiness

Started wondering the other day about the words "Righteousness" and "Holiness," and whether they're interchangeable or if they even mean the same thing.

One source I found stated that, loosely paraphrased, Holiness describes our relationship to God, whereas Righteousness describes our relationship with other people.

So, according to that definition, it's possible for someone to be Righteous without necessarily being Holy at all. But is it possible to be Holy without also being Righteous?

I can't see how that'd be possible at all.