Black box testing - not based on any knowledge of internal design or code. Tests are based on requirements and functionality. is testing without knowledge of the internal workings of the item being tested.  For example, when black box testing is applied to software engineering, the tester would only know the "legal" inputs and what the expected outputs should be, but not how the program actually arrives at those outputs. Simply we can say black box testing is deriving sets of input conditions that will fully exercise the functional requirements for a program  
                           
Following error we identify in Black Box testing
incorrect or missing functions
interface errors
errors in data structures or external database access
Initialization and termination errors.

White box testing - based on knowledge of the internal logic of an application's code. Tests are based on coverage of code statements, branches, paths, and conditions. Use the control structure of procedural design to derive the test cases.

Unit testing - the most 'micro' scale of testing; to test particular functions or code modules. Typically done by the programmer and not by testers, as it requires detailed knowledge of the internal program design and code. Not always easily done unless the application has a well-designed architecture with tight code; may require developing test driver modules or test harnesses. Functional and reliability testing in an Engineering environment. Producing tests for the behavior of components of a product to ensure their correct behavior prior to system integration.

Incremental integration testing- continuous testing of an application as new functionality is added; requires that various aspects of an application's functionality be independent enough to work separately before all parts of the program are completed, or that test drivers be developed as needed; done by programmers or by testers.

Integration testing - testing of combined parts of an application to determine if they function together correctly. The 'parts' can be code modules, individual applications, client and server applications on a network, etc. This type of testing is especially relevant to client/server and distributed systems.    

Functional testing - black-box type testing geared to functional requirements of an application; Validating an application  conforms to its specifications and correctly performs all its required functions. This type of testing should be done by testers. This doesn't mean that the programmers shouldn't check that their code works before releasing it (which of course applies to any stage of testing.) The selective retesting of a software system that has been modified to ensure that any bugs have been fixed and that no other previously-working functions have failed as a result of the reparations and that newly added features have not created problems with previous versions of the software               

System testing - black-box type testing that is based on overall requirements specifications; covers all combined parts of a system.

End-to-End testing - similar to system testing; the 'macro' end of the test scale; involves testing of a complete application environment in a situation that mimics real-world use, such as interacting with a database, using network communications, or interacting with other hardware, applications, or systems if appropriate.

Usability testing - testing for 'user-friendliness'. Clearly this is subjective, and will depend on the targeted end-user or customer. User interviews, surveys, video recording of user sessions, and other techniques can be used. Programmers and testers are usually not appropriate as usability testers.

Sanity testing - typically an initial testing effort to determine if a new software version is performing well enough to accept it for a major testing effort. For example, if the new software is crashing systems every 5 minutes, bogging down systems to a crawl, or destroying databases, the software may not be in a 'sane' enough condition to warrant further testing in its current state. is the primary testing done on the application to find it out whether the application is ready for QA testing

Regression testing - re-testing after fixes or modifications of the software or its environment. It can be difficult to determine how much re-testing is needed, especially near the end of the development cycle. Automated testing tools can be especially useful for this type of testing.

Acceptance testing - final testing based on specifications of the end-user or customer, or based on use by end-users/customers over some limited period of time.

Install/uninstall testing - testing of full, partial, or upgrade install/uninstall processes.

Recovery testing - testing how well a system recovers from crashes, hardware failures, or other catastrophic problems.

Security testing - testing how well the system protects against unauthorized internal or external access, willful damage, etc; may require sophisticated testing techniques.

Compatibility testing - testing how well software performs in a particular hardware/software/operating system/network/etc. environment.

Exploratory testing - often taken to mean a creative, informal software test that is not based on formal test plans or test cases; testers may be learning the software as they test it.

Ad-hoc testing - similar to exploratory testing, but often taken to mean that the testers have significant understanding of the software before testing it.

user acceptance testing - determining if software is satisfactory to an end-user or customer.

Comparison testing - comparing software weaknesses and strengths to competing products.

Alpha testing - testing of an application when development is nearing completion; minor design changes may still be made as a result of such testing. Typically done by end-users or others, not by programmers or testers. & typically made with customer

Beta testing - testing when development and testing are essentially completed and final bugs and problems need to be found before final release. Typically done by end-users or others, not by programmers or testers.
Mutation testing - a method for determining if a set of test data or test cases is useful, by deliberately introducing various code changes ('bugs') and retesting with the original test data/cases to determine if the 'bugs' are detected. Proper implementation requires large computational resources. This testing would be done by end users.

Condition testing - aims to exercise all logical conditions in a program a module.

Conformance testing -Verifying implementation conformance to industry standards. Producing tests for the behavior of an implementation to be sure it provides the portability, interoperability, and/or compatibility a standard defines.