More updates:
A Tennessee judge is refusing to grant a divorce between a man a woman.
http://www.washingtonpost.com/news/morning-mix/wp/2015/09/04/tenn-judge-refuses-to-grant-straight-couple-a-divorce-because-of-gay-marriage/
The judge's legal opinion is basically this:
Tennessee previously had laws regarding marriage (between one man and one woman). These laws were rendered obsolete by the Supreme Court decision.
With the Supreme Court decision, the Federal Government has now "set the law" regarding marriage and states can't have their own marriage laws.
Tennessee currently has laws regarding divorce, but divorce laws vary from state to state. For example, in South Dakota, a marriage partner cannot be forced to grant a divorce from their other partner, even if the other partner has no interest in getting back together; while in California, a person can get a divorce in this matter.
Since the Supreme Court has now "set the law" regarding marriage, the Federal Government now has to "set the law" regarding "what is not a marriage".