They are separate, but the term marriage is often what people fight over.

For example the Catholic Church, the largest sect of Christianity, leader believed that domestic partnerships should be allowed and protected. But the term marriage held a "sanctity" to the church and thus they did not believe in marrying them within the religion.

So if you took the term marriage out of the documents, the issue becomes "I don't believe others should have rights that I have" and even their religion doesnt agree with them. Thus the bullshit of hiding behind freedom of religion to hate/persecute others starts to dissolve.