Large language model (LLM) agents tackle complex tasks through reasoning and interaction with external environments. Agent skills provide persistent, transferable capabilities that guide task planning, inform contextual decisions, support tool use, and enable executable procedures. Yet existing skill-evolution methods largely organize knowledge around skill artifacts, overlooking the functional heterogeneity within individual skills and its implications for knowledge maintenance and use. Inspired by cognitive science, we propose Cognitive Differentiation in Skill Evolution (CDSE), which evolves a unified skill through four functionally distinct yet coordinated components: Meta, Experience, Tool, and Script. CDSE extracts evidence-grounded semantic gradients from successful and failed trajectories, consolidates them by functional role, and applies component-specific updates and validation with cross-component coordination and adaptive invocation. An analysis of 500 top-ranked skill packages shows that 96.8% contain knowledge spanning at least two functional roles. Across six benchmarks, three agent models, and two execution harnesses, CDSE achieves the highest scores in all 36 settings, improving over the Base agent by 7.6 percentage points and the strongest competing method in each setting by 2.6 points on average. Ablation studies further support the importance of functional differentiation and adaptive invocation.

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