I don't think I've seen this "marriage equality" term, but it sounds quite non-specific and stupid. I wonder if it's been introduced because the term "same-sex" is considered hate speech to the more fragile elements of the gender-dysphoria lobby?

As you say, "marriage equality" sounds like it could refer to equality on the basis of some other potentially controversial characteristics: inter-racial marriages, inter-religious marriages, child marriages, "marriages" conducted by a cult leader and not recognised by the state etc? In the UK we also had the "civil partnership" precursor to same-sex marriage, where two men or two women could have a state-backed proxy wedding ceremony which conferred the same permanent legal aspects as marriage. Both "marriage" and "civil partnerships" are now available to same or opposite sex couples in the UK – so does "marriage equality" refer to this kind of conception?

When people deliberately make language more confusing to others, there's usually a dishonest agenda afoot.