To be a pedant, but not to dog-pile, if you want to boil communism down to a statement, that statement is (as Marx points out in the Manifesto) to paraphrase 'Human development would be best if all lived by the maxim, from each according to their abilities, to each according to their needs.' Which is, of course, why reading theory is important.

There is a difference. It's not 'just' 'everyone is equal', as liberals claim their society provides with legal equality, and that from legal equality stems liberty. It is a statement that strips liberals of their claim towards the 'maximization of human liberty', and posits that the giving of real materials to the people who are in need of them, not just ideals in a vacuum, are what maximizes overall human development and liberty.