sanity testing is an Initial effort to check whether the 
application can be tested further without any interruption. 
Basic gui functionality connectivity to database are 
concentrated here.
Smoke Testing covers most crucial functions of the 
application testing carried out check whether most crucial 
functions of the application work fine or not? dont bother 
about the in-depth coverage of each testset. 
Shakeout test : To identify an initial, simple end to end 
test which verifies that a load has been successful and all 
software is accessible and functioning as expected and to 
document this test so that the same test may be run at each 
new build, installation or upgrade.

Sanity Testing:

when the New Build is Released for the testing to the
testing team,initial Build Stability and Basic functionality
testing of the application  is called the Sanity Testing.

Smoke Testing:

All the Test Cycles are completed with the Test Cases and
still has the time for testing then without the test cases
testing the application exhaustively is called Smoke Testing.

Smoke Testing:-Its a shallow and wide approach where by all 
areas of the application without getting into deep,is 
tested.
A smoke test is scripted, either using a written set of 
test or an automated test.
Its a normal health check up to a build of an application 
before taking it to testing depth.

Sanity Testing:-Its a narrow regression test that focus on 
one or a few areas of functionality,its usually narrow and 
deep.
Its usually unscripted,its used to determine a smallsection 
of the apllication is still working after a minor cahnge.

sanity : whether  testing can go further level or not. for 
example your CSS mainframe version8.0, you used to create  
the test data for test case execution.while test case 
execution CSS team have changed their version to 9.0. by 
use of this new version we have to check whether can we 
creat test data as like earlier.this is sanity.

Smoke : today we have one set of code.very next day you 
would intimate by developers said that made some changes on 
the existing code.we have to check the changed code is 
properly done or notwith our test environment. this is 
smoke.

But dnt have idea about shakeout.