Over the millennia there have been many terms for the arrangement whereby one person agrees (or is obliged) to agree to a legal “marriage” arrangement with another person. Historically this period was a betrothal, prior to marriage.
Then along came the 20th century and a two sex pair could move in together and set up a de facto arrangement with as far as I know full legal rights.
Next we have the 21st century where two different pairs – same-sex (SS) and two sex (TS) groups claim the word “marriage”.
Two such different arrangements (SS and TS) cannot be described adequately by the one word “marriage” so how about finding another word as a descriptor for one or the other. Either SSM (same sex marriage) or TSM (two sex marriage). But which gets the word “marriage” and which gets another word – yet unknown?
Fight it out people but logically you can’t have just one word to describe two situations and convey any real meaning.