HYPERINTENSIONAL
Logics in which necessarily equivalent formulas are not interchangeable. A possible-worlds semantics identifies a proposition with a set of worlds, and that identification is what makes 2+2=4 and every other necessary truth the same proposition. The entries here refuse it, and each refuses it by replacing the point of evaluation or the semantic value with something finer: a partial state that exactly verifies, an impossible world where classical laws fail, a content or subject-matter that a formula is about.
The division is organized by what replaces the world. Truthmaker entries evaluate at states with a parthood structure and an exact verification relation. Impossible-worlds entries keep the frame and admit points that violate logic. Content entries make aboutness or variable inclusion a condition on consequence rather than a byproduct of truth preservation.
This is the same kind of move that Team makes and a different instance of it. Team changes what a formula is evaluated at from an assignment to a set of them. Hyperintensional changes it from a world to something with internal structure. Modal changes neither: however fine its accessibility relation, a Kripke frame still identifies a proposition with a set of worlds, and necessary equivalents remain interchangeable there.