Is there a difference? Does one fall under the other?
This is an ejection seat handle
It is engineered to be extremely usable. The labeling is clear, communicative, and unmistakable, and the handle is large and ergonomic.
However, pulling it in a supersonic fighter jet doesn't provide a good user experience. The pilot is very likely to escape the jet safely and survive, so the ejection system will have completed its function successfully and usably, but it is still not a good user experience.
Usablilty means: How easy is your software/website to use. does everybody understand the concept directly or do you need to provide a manual?
User experience means: how fun or exciting is it to use your product.
As an example imagine an alarm clock:
Good Usability: The alarm is easy to be set.
Good User experience: It wakes you up by using birds' twitter, soft music and emitting a warm light instead of using a sound like an abulance siren on a volume that will even wake your neighbors 3 blocks away.
I also think, that good usability is part of a good user experience, since you don't have a good time with a product, if it is not easy to use.