This is the wording of the "Defense of Marriage" amendment to the Michigan State Constitution:

To secure and preserve the benefits of marriage for our society and for future generations of children, the union of one man and one woman in marriage shall be the only agreement recognized as a marriage or similar union for any purpose.

It isn't aimed at seeing that same-sex unions aren't called marriage; it is aimed at denying any legal recognition whatever to same-sex couples. The proponents of the act said it would not deny dependent benefits to same-sex partners. I said it would. The resultant court cases I know of so far are aimed at preventing taxpayer supported institutions from paying partner benefits; I fully expect someone to push for criminalisation of the payment of partner benefits by private employers.