Sanity Testing: 
                 Initial testing is called as sanity 
testing. After completing the test initially we will test 
the givem module is that up to the mark or no that is 
called sanity testing.


Smoke Testing:
               Smoke testing is nothing but before 
releasing the project the final testing is done that 
testing is  called smoke.


Based on the organization this will we wise versa in some 
organizations the name will be in opposite but the theme is 
the same.

smoke testing:  consider as a positive testing.In this 
testing will do short testing.

Sanity testing : consider as a  negative testing .sanity 
testing is to verify whether requirement are met or 
not ,checking all features breadth- first.

i think both are same.
sanity testing: After receiving the build, testers has to go 
for sanity testing, in order to ensure that build is stable.


Shankar

Sanity Testing:It's generally is a subset of regression 
testing.It is in-depth testing of that module for which the 
errors have been rectified. If the error is in one function 
of the module we will test that function as well as the 
whole module.


Smoke Testing: It is done to ascertain if the build is 
stable and can be used for further testing.it is done to 
find wheter the basic functionality of the program is 
stable.

Sanity testing: A tester conduct testing on the received initial build to verify the basic functionalities of our application.It is also known as Build verification testing.

Smoke testing: A tester are validating the negative and positive functionalities of  a application.