sanity testing and smoke testing are similar(it takes same
time).
 (I) sanity testing: 
                 It is a  quick test phase done after the
build release to testing to make sure that build is ready
through testing
  1) sanity test is carriedout to test the testability of
the build 
  2) Every build release from development should be followed
by sanity testing
  3) during sanity testing we test the installation
,application launchimg & navigation through the pages
  4) if sanity testing is failed we stop the testing &
reject the build
  5) for sanity testing we genrally maintain check list  .

NOTE: sanity testing is always carriedout on the clean testbed

 (II)smoke testing:
                    testing the complete set of requiements
on the total project

   1) During system testing if any bugs are identified we
will report the to developers & proceed with the testing 
 
   2) After the sys testing is completed all the bugs will
be fixed and a new release will be given to the testing team

   3) when a re-release is given for testing we test the
bugs,dependencies,core functionalities of the project

   4) when sys testing  is passed acceptany testing will be
started.
    all acceptany testing realse aaaaaaaaaaaaa7 maintain
will be followed.

Sanity testing is a subset of regression testing, which is 
used to prove the application is functioning according to 
specifications.
Whereas Smoke testing is done prior to the regression 
testing, or when the build is ready for testing. It is used 
to verify whether most crucial functions work fine, so that 
the build can be accepted for further testing.

Sanity test will do the build is ready to realse to the 
test environment.
We can  do the sanity test, in initial stage itself, 
whether the build is able to test or not.

Smoke testing : we will do the  smoke testing, if there is 
no time lines that but we need to complete the testing, 
that time we will test the main functionalities of the 
application. This is the smoke testing.

If I am wrong please let me know.