sanity testing is the process of testing the build released 
by the developer,to accept it for complete testing or 
not.In sanity testing first basic functionality will be 
tested.

smoke testing covers the most basic features of an 
application.
failed test cases of smoke will be executed as sanity test 
cases in the next build.

smoke is "to check the basic functionlity of the 
applicaiton"
  Sanity "to check the complete functionlity of the 
application"

The basic difference is :
Sanity testing is not scripted
Smoke testing is scripted

sanity testing is a cursory testing.in this testing a 
tester test the basic functionality of the software.

while in smoke testing ,tester test the major functionality 
of the application in depth.

We are conducting sanity testing,after receiving build from 
development team.In sanity testing we are verifying the 
basic/primary functionalities are working properluy to 
conduct testing.It is also called tester accepting testing 
or initial testing.
where Smoketesting,we are verifying the main 
functionalities of the build/AUT.i.e In customer point of 
view what are main features of the build.while Acceptance 
testing on what factors the final user/customer 
concerntrating functionalities.
And Smoketesting conducted on every new release of the 
build, where as sanity is optional.