At least in terms of conferring powerful legal rights and obligation, especially in the case of a heterosexual couple, the word marriage, is exclusively granted by governments, be they counties, State, Countries, and such are by in large international in scope. Its why you have to apply for as wedding license, meet certain age, health, and time restrictions, and thereafter, the signed marriage certificate is usually stored by the county court where you got married. l Think about it, in event of divorce, if marriage was not State, National and often international, one or the other parties to the marriage could simply leave the State, or their nation and get legally married again without the bother of getting a divorce. And its absurd to think that a church has any force of law to protect the legal rights of the abandoned partner in any marriage or their children.
Maybe some religions have the right to deny the wedding ceremony within their church, but they still can't prevent two people from being married outside of their church. The Roman Catholic church often denies remarriages to a divorced catholic, without a papal permission, and could then deny the married couple permission to worship in their church.
But, still, its why US courts traditionally dislike the term civil union for gay and Lesbian couples. Because it too similar to the other Jim Crowe law term of separate but equal education. In short, its either a marriage that confers all the legal rights and obligations in a marriage or its a sham. With the other problem being, if a gay or Lesbian couple get married in another State where such marriages are legal, how can Texas deny them the same legal rights? When Texas can't do the same with any legally married heterosexual couple.