When a cognitive system modifies its own functioning, what exactly does it modify: a low-level rule, a control rule, or the norm that evaluates its own revisions? Cognitive science describes executive control, metacognition, and hierarchical learning with precision, but lacks a formal framework distinguishing these targets of transformation. Contemporary artificial intelligence likewise exhibits self-modification without common criteria for comparison with biological cognition. We show that the question of what counts as a self-modifying system entails a minimal structure: a hierarchy of rules, a fixed core, and a distinction between effective rules, represented rules, and causally accessible rules. Four regimes are identified: (1) action without modification, (2) low-level modification, (3) structural modification, and (4) teleological revision. Each regime is anchored in a cognitive phenomenon and a corresponding artificial system. Applied to humans, the framework yields a central result: a crossing of opacities. Humans have self-representation and causal power concentrated at upper hierarchical levels, while operational levels remain largely opaque. Reflexive artificial systems display the inverse profile: rich representation and causal access at operational levels, but none at the highest evaluative level. This crossed asymmetry provides a structural signature for human-AI comparison. The framework also offers insight into artificial consciousness, with higher-order theories and Attention Schema Theory as special cases. We derive four testable predictions and identify four open problems: the independence of transformativity and autonomy, the viability of self-modification, the teleological lock, and identity under transformation.