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I would say that the General Linear Model includes most of the tests that you are talking about. It collects them together under one hat, so many standard models become special cases.

In these tests, we are testing for certain values of parameters in these models. So the GLM includes these parametric tests within the framework of models it specifies.

Of course the GLM does not cover all models, so you would need specific tests for other models, which you can derive based on the model's assumptions.

The Kolmogorov-Smirnoff test is a non-parametric test. Non-parametric tests are yet another group of tests to look into.

This is a non-exhaustive list, and this is within a frequentist setting. If you go into Bayesian inference this all changes.