If you have dual citizenship do you need an EAD as well?

I'm just curious because I have a friend who has a social number, owns a home here in the US, his family owns a business, but he has an EAD too. Or is it possible to have a social security number without being a full citizen? I'm confused on this and would like some clarification. I've tried looking up info on EAD, but I can't seem to figure this out.