The definition of marriage should remain as it is - the union of an adult male and female not related by blood. Homosexuals should be given a parallel institution for themselves, and them alone. It would have all the rights and duties of heterosexual marriage but would not be called “marriage”. It would be called “companionage”, and the participants would not be bride and groom but “companions”. This separate institution should have the force of law and be secured by legal contracts and ceremonies, conducted by the state. Religious marriages will continue to be recognized by the state with whatever restrictions the particular religion chooses to place on them, as entered into by adults of their own free will. That is all.
You have identified the real issue. The issue is not "Gay or Same-Sex Marriage" (which is an oxymoron), but the actual definition of marriage itself.