The definition of the words is in how it is used, bardock.
And when people talk about 'rights' in this context, they generally mean a set of aspirations that all people should have. And if one of the things in that list is what I mention above, that people should have the right to marry the consenting adult of their (mutual) choice, then the rights of straight people are currently met by the American legal system and the rights of gay people are not, even though the law is the same for both.
Hence inequality. Hence a demand for equality.
Laws are a means to an end, after all.