The difference between smoke and sanity testing

My experience of executing the Smoke and Sanity testing has been the following:

Smoke Test:
When a build is received, a smoke test is run to ascertain if the build is stable and it can be considered for further testing. Smoke testing can be done for testing the stability of any interim build. Smoke testing can be executed for platform qualification tests.

Sanity Test:
Once a new build is obtained with minor revisions, instead of doing a through regression, sanity test is performed so as to ascertain the build has indeed rectified the issues and no further issue has been introduced by the fixes. It’s generally a subset of regression testing and a group of test cases are executed that are related with the changes made to the app.

Generally, when multiple cycles of testing are executed, sanity testing may be done during the later cycles after through regression cycles.