Inside-Out and Outside-In are fairly rare terms, more often I have heard/read about Classic school and London school.
• Inside-Out (Classic school, bottom-up): you begin at component/class level (inside) and add tests to requirements. As the code evolves (due to refactorings), new collaborators, interactions and other components appear. TDD guides the design completely.
• Outside-In (London school, top-down or “mockist TDD” as Martin Fowler would call it): you know about the interactions and collaborators upfront (especially those at top levels) and start there (top level), mocking necessary dependencies. With every finished component, you move to the previously mocked collaborators and start with TDD again there, creating actual implementations (which, even though used, were not needed before thanks to abstractions). Note that outside-in approach goes well with YAGNI principle.
