These are such great books!
I'll go further by clarifying the semantics of Meg's comment and expounding on the answer you first received. The words "like" and "equal" do not have the same meanings. For instance, in the 1960's in America, black students went to school "like" white students, the had public water fountains "like" everyone else, and they could ride public transportation "like" everyone else. However, these were not "equal" circumstances. Black schools lacked needed supplies and resources like books and qualified teachers, water fountains for blacks in public were only for blacks--they may not always be serviced or working properly or kept clean, and blacks were expected to ride in the back of public buses and even give up their seats when the bus was overcrowded to white passengers. "Like", yes, but "equal"?--absolutely not.
Now, go back and read the section where Meg makes her comment and see if you follow better.
Meg is explaining a core concept in rights theory, one that is still very active in today's politics. The idea that everyone is equal is that everyone has the same rights, and the same opportunities within the legal and social structure. No one is preferred, and no one has special rights. The idea that everyone is the same imposes a set of shared characteristics and outcomes. Everyone eats the same food, wears the same clothes, etc. They are the different definitions of equality used by a republic (like America) and a totalitarian state.