From my perspective User Experience is the science (and art) of creating functionality and information that helps the user to carry out particular tasks. In the world of websites and native mobile device applications (apps) this revolves around: understanding users & their needs, mapping user flows through key tasks, creating wire-frames, designing the interface and testing it to ensure it does what it should as well as it possibly can.
This is wider task of mapping the entire path of the customer from start to finish E.g. from a point where they are not the customer and perhaps not even cognisant of your product or service, through to the stages where they have become a customer and beyond. There are a lot of different models for how this customer journey can be represented, but regardless it is useful to map this journey for your business.
So do the two cross-over? Yes, in my opinion they definitely do and in fact I believe you cannot properly create the ideal User Experience unless you properly understand the Customer Journey. By this I mean that any UX work done needs to know where it fits in the wider picture of things, what the situation is for the user beforehand and what the end goal is.
For example, if you are creating the interface for a ticket vending machine at a sports ground, it would no-doubt help your UX resource to understand why the user is there, what they should (or shouldn't) have done previously and what they are going on to do. In this example, the creation of the vending unit is not to raise awareness, to educate or to entertain, it is there to help the customer who may already have purchased a ticket to get it printed out as efficiently as possible so that they can go and have the bigger experience they have paid for.
Either way, I suggest that to truly deliver the best for your customers you need to create both and validate them in as many ways as possible, both before and after you have delivered.