Alpha Testing
-------------
Testing of a software product or system conducted at the
development site by the customer(End user)

Beta Testing
-------------
Testing of an application when development & testing are
essentially completed and final bugs and problems need to be
found before the final release.

Typically it is done by end users not by testers or developers.

alpha testing:test the application by the customer
representative at the development environment is called as
alpha testing.

Beta testing:Test the application by the customer
representative at the customer environment is called as beta
testing

Both Alpha and Beta testing comes under User Acceptance
testing. To check project functionality and application
functionality at development area with client is call alpha
testing where as check the project functionality and
application functionality at client are with end user is
call beta testing