Difference between regression, sanity and smoke tests

Regression test: It is a type of application testing that is used to verify any modification or update in an application without affecting the overall working functionality of the said application. It is usually done at the last stage of UAT. 

Sanity test:  It is a subset of regression testing. After receiving the software build, sanity is to ensure the code changes introduced are working as expected. 

Smoke test: It is a quick test to run through the application to ensure each function is working according to the business requirements. Normally, it takes 10-15 minutes to run through the application.