Alpha Testing & Beta testing are types of UAT.

Alpha Testing : Testing done at developers site, when application is nearing completion. some minor changes in design is still be possible as a result of Alpha testing, it is done by tester in coordination with customer

Beta testing : Testing done at client or customers place before the release of the product in complete required environment to check the product is working as per requirement or specification, it is done by some selected user from the client side.