Regression testing -Regression testing  is the process of testing changes to computer programs to make sure that the older programming still works with the new changes. Regression testing is a normal part of the program development process and, in larger companies, is done by code testing specialists. Test department coders develop code test scenarios and exercises that will test new units of code after they have been written. These test cases form what becomes the test bucket. Before a new version of a software product is released, the old test cases are run against the new version to make sure that all the old capabilities still work. The reason they might not work is because changing or adding new code to a program can easily introduce errors into code that is not intended to be changed.
What we do in regression testing?

• Rerunning the previously conducted tests
• Comparing current results with previously executed test results.

 Functional Testing
"The objective of function test is to measure the quality of the functional (business) components of the system". Tests verify that the system behaves correctly from the user / business perspective and functions according to the requirements, models, storyboards, or any other design paradigm used to specify the application. The function test must determine if each component or business event: performs in accordance to the specifications, responds correctly to all conditions that may be presented by incoming events / data, moves data correctly from one business event to the next (including data stores), and that business events are initiated in the order required to meet the business objectives of the system.

Smoke Testing 

A Smoke Test is a process of validating code changes before the changes are checked into the product’s official source code. That means it is usually done when a bug fixing or change request is executed. Smoke Testing is also called Build Verification Test or Rattle Test.

This can be done either by developers or testers. If developers do this, it should be done before the release of product (or “build”) and if testers, - done before moving to next types of testing. Nowadays these tests are performed by some automated system which is included in the build mechanism.

Validation and Verification testing -Verification Testing: It is the set of activities which ensures that the software correctly implements a specific function.
Validation Testing: It is the different set of activities which ensures that the software that has been built is traceable to the client requirements.
Verification is mostly done by the developer, and all white box testing techniques can be used for verification testing.
Validation Testing is the responsibility of the tester, and all the tests done in block box testing will be treated as validation tests.