I think you'll find that different people will have different opinions about this, so while this is probably just my opinion, I will try to explain it in the most objective way I can think of.
When you approach design from an 'engineering' perspective, it is about providing a solution to a problem that comes from first principles. That is, you come up with a solution based on facts and ideas that you already know and create a solution around it based on known constraints. When you approach design from a 'creative' perspective, it is about experimenting with ideas and see which of the possible solutions best fits the requirements.
However, the term that you used (usability) covers only one aspect of what is considered a multi-faceted challenge that is user experience design. And the term user centered design is only one perspective is what is considered a multi-disciplinary challenge that is part of customer experience and/or service design.
For me the best way to think about it is that UX or UCD are design philosophies, and that UE is one particular model that solves one aspect of the user experience design problem domain.