I khow that UX - How user feels about using a product. UI-how easy it is to use a product and how convenient is a product to end user. Is it the same or not?
UX (User Experience) is the process of creating and building software products (web/app/etc) that provide relevant experiences to users. It includes aspects of branding, design (UI), usability and function. In simple, usuability is subset of UX.
So when you do Usability testing, it's only checking if product is easy to use with real users.
For UX testing, you must care more aspects such as pleasure of real users, efficiency of functions, GUI, etc.
Both the term generally confuse the testers in software testing company. Usability testing is a part of User experience testing. Usability testing is being performed to determine system's ease of access by user.
User experience testing is being performed to test different aspects of user experience to determine the best way for a system and its elements to interact with its audience.
For example, let say any page having some action controls and inputs fields:- Usability testing determine that all the controls are meaningful to end user while using the application. User experience majorly focus on look and feel of the app. Making sure UI content, color,icons, images used in the system are aesthetically pleasing.