We do sanity or smoke test when we receive the build for 
the first time. Before accepting the build we test the 
basic functionality of the build. This process is called 
either sanity of smoke. Both are alomost similar.

Sanity testing->Testing the application for the first 
time.Or it is called an adhoc testing.Not in a position to 
test the application in details.
Smoke testing-Testing only the major functionalities of the 
application.Smoke testing is done when ever a new build is 
happening.Or it is an example of regression test.Usually we 
can use automation testing tools for performing smoke 
testing.

Situation-->A new build has been released(New version).The 
new changes implemented by the development team has been 
tested and is working fine(Sanity testing).But due to the 
new changes,Some existiong functionalities is getting failed
(Smoke testing).

both are same as per my knowledge

First clear with sanity and smoke.

Smoke testing: 
             its also called as build verification test. As 
soon as we get the build we are testing whether the build 
is in testable condition or not.

Sanity testing:
              Its testing the major functionalities in the 
application. You ll go for sanity if u dont find enough 
time to do full regression test. 

so there is no chance for sanity to pass, if smoke fails.

sanity test checks the existence of functionality where as 
smoke test checks whether functionality is working or not ..

since smoke test checks the functionalities work so the 
test cases which passed during sanity test will sometime 
fails.

jay,
IBM

in smoke testing we check all the critical functionalities 
such as all p0(high)
where as in sanity we check both critical and major 
functionalities. p0 and p1.
smoke is also called as bvt and sanity is a part of system 
test which will be done before the acceptence test.