smoke test: Testing the application if it  is wokring 
properlly or not is called smoke test. Here we test for the 
stability of the application for further testing.
Eg: The main purpose of yahoo website is to login, check 
mails, send mails and logout. Wen a build is released for 
that, we first check for its basic functionality. here, it 
is logging in, checking and sending mails and logging out.
 
sanity test: Testing the application if everything is there 
in applicatioin or not is called sanity testing.
Eg: For the same above example, sanity testing is to check 
whether login fields, all buttons, background colors etc 
are there as per the requirements or not.

Plz correct me if i am wrong... 

smoke test: Testing the application before the build has 
given to the testing whether the appliocation is working 
properly or not at development side

Sanity test: Testing the application once after build is 
recieved from development team for further tests at testing 
environment wheteher the  bulid is stable or not and its 
basic features r working properly

Smoke Testing : Testing the build for its basic 
functionality is called smoke testing. We perform this 
testing for knowing the stability of the released build 
once we find it stable then deeper functionality can be 
performed.

 Sanity Testing : It's a Narrow Regression Testing its 
mainly performed on one or few selected areas where 
modification is done to check whether the previous bugs 
have been fixed or not.

rather i'll suggest 1 st answer is more appropriate for 
this question