Star Law and the UPF

Recently in the main forum there has been a discussion of just what is the distinction between Star Law and the United Planetary Federation.  That's something we could work on here, too.  Is Star Law just a branch of the UPF, like UN Peacekeeping Force?  Is it like Interpol?  I've always viewed Star Law as similar to old west marshalls: they are a branch of the federal government but given jurisprudence over all states and territories.  Also, I see Star Law as existing before the UPF, and as a result were later brought under the auspices of that body.  Thoughts?