Alpha testing and beta testing are the types of user 
acceptance testing.

Alpha Testing:It is performed by client at devloper's 
site.It is prerelease testing.Normally alpha testing is 
performed at nearing the development completion.

Beta Testing:It is performed by client at their own site.It 
is performed to verify product meets the user requirements 
and to take important decision about release of software.

Sanity testing:It is cursive testing.It is subset of 
regression testing.Sanity testing is narrow and deep.e.g 
After receiving new build with minor changes sanity testing 
is performed to ensure fixes are indeed fixed and no other 
defects are introduced as a result of changes.After 
performing several cycles of regression testing sanity 
testing can be performed at later cycle.