Becky and Sara initially seem like polar opposites: one is a rich, doted-upon, and highly educated girl; and one is a rough scullery maid. When they forge a friendship, Becky can't believe someone like Sara would ever associate with her, even though Sara assures her that they're both little girls so they can't be that different.
But eventually, Sara is proved (mostly) right: "Oh, Becky … I told you we were just the same—only two little girls—just two little girls. You see how true it is. There's no difference now. I'm not a princess anymore" (7.204).
Of course, there's still that tricky class business that makes Sara turn back into a princess while Becky is still only a maid. But, hey. You can't expect too much out of nineteenth-century England.