Dimensions of Test Categorization

System testing in general, and software testing in particular, is often grouped into categories such as "unit test", "smoke test", and "regression test". How do these categories relate to one another? Some, such as "unit test" and "e2e test", are mutually exclusive, while others, like "e2e test" and "regression test" can overlap -- a test can belong to both. This distinction comes from the dimension in which the categories are defined, a concept that is rarely discussed or clarified. Below is a list of these dimensions and their respective categories. Each dimension is independent of the others.

Categorization by the granularity of the system component being tested

Unit test: Testing small pieces of code in isolation, without dependencies
Integration test: Testing how components work together
E2E test: Testing the system as a whole, from the user's perspective

Categorization by "existing feature" vs "new or modified feature"

Regression testing: Testing of existing features to ensure they still work after making any code change
New or modified (including fixed) feature testing

Categorization by the breadth of the application features being tested

Smoke / sanity testing: Quick test of only the most important features
Feature / partial testing: Testing of selected features
Comprehensive / thorough / exhaustive / full testing: Testing all features

Categorization by "how" the test is conducted

Manual testing
Automated testing

Categorization by the quality aspect

Functional testing
Performance testing
Security testing
Usability testing
etc.

An example:
An e2e test may also be either a regression or a new feature test, and may also be a functional or a performance test, and may also be either manually executed or automated.