Alpha Testing : testing is going to done within the 
developement environment (i.e in the organisation itself)

Beta TYesting : testing is going to done in the client 
environment i.e testing is done by the client uesers

Before delivering the application to the client, the final 
level of testing is the user acceptance testing.
There are 2 ways to conduct User acceptance testing
alpha testing and beta testing
alpha testing:testing of an application when the 
development is nearly complete. Minor design changes can 
still be made as a result of alpha testing.Developers,test 
engg form an independent team along with  the customer site 
representatives.
beta testing:testing of an application where the 
development and testing are essentially complete and final 
defects and problems need to be found out before the final 
release.End-user typically perform beta testing

alpha esting means within in the company or house or 
offsite testing.

beta testing means client side testing or outsie testing, 
onsite testing.