Sanity Testing: I)To test the major functionalities of the 
application to confirm the build is ready for testing.
II) this Sanity testing is done before releasing to the 
Testing.

Smoke Testing:I) Here also we do check the major 
functionalities of the application to confirm that the 
build is ready for Client Release.
II) Smoke Testing is done before releasing to the client.

Please correct me if iam wrong.

As far as I know smoke testing is done by developers b4 
releasing the build to testers and sanity is done by 
testers to check whether the major functionality is working 
or not to carry out further testing.

smoke testing is to test the stability of the build.
after receiving the build our testers are doing sanity
testing for stability of the build.After doing the sanity
testing then only our test engineers will conform that we
can do testing(FUNCTIONAL,NON-FUNCTIONAL,USABILITY) on the
build.

sanity testing is nothing but weather the application  is  
built is stable r not as per  the URS. smoke testing is 
check total functionlity of that built.

Sanity Testing
--------------

Once the release made from developer's end, testers have to 
do a sanity testing to confirm that we can able to continue 
further testing in the release made. (Build is stable or 
not for testing)

Smoke Testing
-------------

Before releaseing to client we have to do Smoke Testing to 
confirm there is no smoke in the build which is getting 
released to client.

Sanity and Smoke testing both are same and in this we 
perform Buid verification means that the given build is 
ready to perform testing or not... 

People call it as Smoke tesiting or Sanity testing or Buid 
verification testing.