Can someone explain why some 2-engine UA planes of a given model have ETOPS certification (or at least have ETOPS printed on the front wheel well) and others don't seem to? If all of UA's 777s have the same engines, what would make the difference?

By the same token, what makes one A320 an "overwater" model and others not? Does it have to do solely with whether lifejackets are aboard in addition to floatable seat cushions?