Alpha and Beta testing is a part of the User Acceptance 
Testing.
But Alpha Testing is done when the application is nearly 
complete and so minor design changes can still be made here.
Developers,test engineers and the customer site 
representatives involve in this.
WHERE AS
Beta testing is testing an application when the development 
and testing are essentially complete and final problems and 
defects are to be sorted out.End-User typically involve 
here.
It is done at the client site.