What you describe is more like the user interface. The mockups and the motion the flow etc... are the result of how you are going to communicate the desired user experience.
User Experience is what emotions, what state of mind or usability you want to achieve for the user that will interact with your website/app or whatever you design.
So the person who is UX designer should get (probably from marketing research) of what do your target audience except to receive(or what you want them to receive) upon using your product
A simplistic example would be like this:
A client (lets say a bank) wants to improve the brand image and give the feeling to the customers that is:
- up to date
- and cares about its customers
Now the marketing department should research the target audience and give briefing to the user experience.
Then the user experience department will analyze and describe what should be done to cover the demands of the client to improve the brand image
a simplistic approach would be
- modern ---> this means it must be something for the smart phones(an app or an accessory)
- up to date ----> this means the design of it should follow latest trends
- cares about customer ----> this means (for a bank customer) fast and secure transanctions, so whatever you create must scream I'm secure I'm fast.
after this is done the user experience department briefs the design department and they produce the User Interface for the User Experience described.
Hope this helps you abit, and again i point out that this is simplistic explanation