The picture clarify a lot: https://alperenkeles.com/posts/vocab-for-testing/types-of-testing.png

How to define the vocabulary?

• scope (I/O, stateful or stateless, isomorphic)
• purpose and hypotheses: functional correctness, time of execution, security, system resilience,
• oracles: humans with tinker testing; examples; inline assertions; properties
• methods: static analysis, enumeration (cover all posibility), randomness, environment simulation (Deterministic Simulation Testing)

Follow-Up: https://matklad.github.io/2022/07/04/unit-and-integration-tests.html

Think about unit and integration-testing in terms of:

• Purity corresponds to the amount of generalized IO the test is doing and is correlated with desirable metrics, namely performance and resilience.
• Extent corresponds to the amount of code the test exercises. Extent somewhat correlates with impurity, but generally does not directly affect performance.