Prompt Engineering and Context Engineering are complementary sides of the same LLM interaction process: the former crafts efficient input phrasing (like Zero-shot or Chain-of-Thought) that's cheaper and sufficient for most tasks due to minimal token usage, while the latter builds richer data environments for complex scenarios. Start with cost-effective Prompt Engineering for 80% of needs, escalating to Context Engineering only when extended knowledge or tools are required, as in your LM-Studio caching optimizations.