User Experience (UX) deals with people interacting with your product and the experience they receive from that interaction. UX is measured with metrics like: success rate, error rate, abandonment rate, time to complete task, and (since we deal in digital) clicks to completion.
Customer Experience (CX), in contrast, encompasses all the interactions a person has with your brand. It might be measured in: overall experience, likelihood to continue use, and likelihood to recommend to others. In essence, UX is part of a broader CX, but CX contains some aspects outside of a product that UX does not.