I think that taking Williams' work and applying it to your quote would be a good exercise. The idea of two people living in different realities is quite evident in A Streetcar Named Desire. Blanche and Stanley live in parallel spheres of existence, with each one striving to have their own realm deemed supreme by Stella. They battle one another with their multiple perceptions of reality. It's more than being "different" with alternate beliefs and choices. Both Stanley and Blanche have diametrically opposed views of the universe and the people in it. Neither one can afford to have the other's exist, and their dramatic interplay is more like a dance of death where one of their visions have to perish. In Blanche's world, a perception of reality where Belle Reve and stately Southern manors are where gentlemen and rules of decor are strictly respected, Stanley would be nothing more than a servant, if that. His crass and rude mannerisms would have been rejected as the very representation of being "uncivilized" and "undignified." In Blanche's reality, her sense of self makes "sense" and it is a world that gives her comfort, precisely because it is a view of reality that is absent in the modern setting.
Stanley's perception of reality is one where the realpolitik and pragmatic nature of the world emboldens the strong and the forceful. In Stanley's perception of reality, a working class guy with Polish parents can make it in America because everyone has the same starting point to eke out an existence. Blanche's world represents the old order where social stratification was not an expression of dignity and class, as much as it was to strangle out people from trying to appropriate their own world and empower themselves. For Stanley, his impression of reality is rooted in power and the fact that he holds it in his world is a reflection of the correct values that his world holds. In Stanley's perception of reality, Blanche is nothing more than a "gold digger" or some other rich "hasbeen" who is living off of some means of income that he has to not only discover, but appropriate for himself.
Both of them see reality differently and do so in a manner that rejects "the other." They cannot share the same vision of reality becuase each one's reality is rooted in the other's rejection.