smok testing is a entry level testing means here we will 
check whether our system is ready for entering into testing 
phase life cycle for e.g ok button on gui or proper error 
mesage etc.

where sanity testing is  a testing where we will perform 
wide testing means know for detail for that perticular 
error but in smok we will not going into detail but here 
we'll.

Smoke- A process of testing whether the build is ready for
further testing or not
 
Sanity - A process of testing whether the code is ready for
further testing or not

Smoke Testing:  This is the initial testing performed on 
the build.  During this testing, the test engineer will 
check for availability of all major functionalities.  If 
any major functionality is missing, he will reject the 
build and request for a patch.

Sanity Testing:  During sanity testing, a tester will look 
for extra functionalities in the build, as the build is not 
supposed to have any extra functionality.  This testing is 
also called garbage testing.

Sanity Testing: It means whether the build is ready for
testing or not.
It is a entry leval testing and if it is failed Test lead 
reject the build immediately.

smoke testing is a deep testingand it is also entry level
testing.

Developers do smoke Testing
Testers do sanity Testing

I think this is an detailed explination for Manju’s answer.

Sanity testing:
                     It is also called as Build Acceptence 
Testing or Build Verification Testing.
If we conduct a overall testing on the released build 
inorder to check whether it is proper for further detailed 
testing or not. It is conducted by test engineers.

Smoke testing:
                        If the same thing done by 
developers before releasing the build then it is called as 
Smoke testing.


In my view both smoke testing and sanity testing is same.