Think of it this way. Eliza's poor and she knows it, and she wants to get off the street. Clara's, well, kind of wealthy, but her family's on the decline, and she's clueless. Eliza's tough; Clara's weak – heck, she won't even go out in the rain to fetch a cab. At the beginning of the play, Clara represents all that Eliza isn't and can't be thanks to her position in society. When we first meet the two of them in Covent Garden, Shaw tells us that Eliza's features are "no worse than" Clara's, but Eliza's dirtiness keeps her from looking like an equal (1.29). By play's end, we find out that Eliza is her equal – and more, that their initial differences were really just the result of poverty and neglect.