Sanity vs Smoke Testing

Smoke Test:

When a build is received, a smoke test is run to check for 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.

Sanity testing:

Once a new build is obtained with minor revisions, instead of doing a through regression, a sanity is performed so as to ascertain the build has indeed rectified the issues and no further issue has been introduced by the fixes.  Its 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.