Acceptance testing :This testing is done to check whether 
the client or user is accepting the product or not

Alpha testing :The testing done by developer's after the 
development phase is completed

Beta Testing: The testing done in the absence of 
developer's in user site.

Alpha and beta testings come under Acceptance Testing.

Alpha testing is actual or simulation of the application 
testing at the developer's site. Usually done by the test 
team or users/customer's. After this, the application is 
send for Beta testing.

Beta testing is done at the customer's site. The 
application is released to a limited audience.Beta versions 
are released to public for feedback.

alpha testing and beta testing both comes under the 
acceptence testing 
alpha testing is the testing where the client would be 
called for demo before accepting the product. the client 
conducts this test in the developers place
Beta testing is the testing where the client of that 
particular project conducts testing at one or more customer 
sites and the customers records the problem and reports it 
to the vendor and get them modified