Both of these are more or less the same.  Checking the 
basic functionalities of the build after deploying the code 
is called smoke or sanity testing.

Hope im rite.

Sanity Testing: In a application, take up a functionality
and get into deeper roots of the same. Testing a single
functionality covering its impact on the whole application
is termed as Sanity Testing.Its generally a subset of
regression testing and a group of test cases are executed
that are related with the changes made to the application.

Smoke Testing: Testing the build and check for the minor or
major smoke(nonfunctional)coming out, is termed as Smoke
Testing.Smoke testing can be done for testing the stability
of any interim build.

Sanity testing - Testing to determine if a new software
version is performing well enough to accept it for a major
testing  effort. If application is crashing for initial use
then system is not stable enough for further testing and
build or application is assigned to fix.