Usability testing and User Acceptance testing serve the same purpose of delivering quality product. But, they both vary slightly.
Usability testing is to be performed to ensure if the users can use the product with ease and it is ready to deliver. The Tester mimics the user and tries to find flaws in usability of product.
User Acceptance Testing(UAT) is performed by Client to make sure the product is working fine and matching with agreed upon requirements. Beta Testing is part of UAT Testing.