sanity testing:
         before going to test the build, test whether the 
build is ready for further major testing.In short v can say 
it is basic testing.

Smoke testing:
  the build is moving from one phase to another phase (dev 
to testing ) then v test the build is called smoke testing

Sanity:

 Whether a development team released build is STABLE for
complete testing or not.

Smoke:

 Its a extra shakeup in sanity testing.
 In this level testing team reject a build with reason when
that build is not working to be applied complete testing.

In general,

Build-->sanity/smoke testing-->functional & System testing

Smoke Testing : is done to ensure that basic 
functionalities is not affected in the build.

Sanity Testing : is done to ensure that the existing 
fuctionalities are not affected by the new fuctionalities 
added in the build.

Smoke Testing : After receiving any build smoke testing is
performed to determine program launches ,interfaces are
available & responsive.

Sanity Testing : Sanity testing is basic functionality
testing.It is performed in order to ensure basic
functionality is working properly before considering build
or application for through testing.Also if smoke testing
fails then it is impossible to perform sanity testing.

Basically both these testing are performed to ensure our
testing time & efforts should not waste.