Maybe. Sometimes ethical egoism sounds like it says that you should be selfish. If that's the case, than no, they are not the same. But sometimes it just sounds like it says you should do whatever you want to do, even if that includes helping others. If that's the case, they sound the same to me.

edit: Actually, that's not quite right. On the second version, egoism give the same answer as EY's metaethics for all agents who have "what is right" as their terminal values, but NOT for any other agent. Egoism in this sense defines "should" as "should_X" where X is the agent asking what should be done. For EY, "should" is always "should_human" no matter who is asking the question.