In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.
Analogously, what could be called a semi-marriage is like a marriage, but without the requirement that the persons be of opposite sex. (Compare here.) How would this work?
First, a marriage is also a semi-marriage so the legal requirements that apply to a semi-marriage apply to a marriage as well. For example, age requirements for semi-marriages would apply to marriages also.
Second, a semi-marriage is not necessarily a marriage so one cannot assume that every property of a marriage is also a property of a semi-marriage. Each property of a marriage must be evaluated to determine if it applies to a semi-marriage. For example, a business that offers services for marriage ceremonies may not need to offer the same services to semi-marriage ceremonies.
The law may focus on semi-marriage rather than marriage because semi-marriage has a larger extent. Yet it would be possible for some laws to apply to marriages but not semi-marriages. The decision as to which way to go is up to the political process.
In the U.S. since the Obergefell decision, civil marriage is semi-marriage.