Many natural and artificial entities can be predicted and explained both mechanistically, in term of parts and proximate causal processes, as well as functionally, in terms of functions and goals. Do these distinct “stances” or “modes of construal” support fundamentally different kinds of understanding? Based on recent work in epistemology and philosophy of science, as well as empirical evidence from cognitive and developmental psychology, we argue for what we call the “weak differentiation thesis”: the claim that mechanistic and functional understanding are distinct in that they involve importantly different objects. We also consider more tentative arguments for the “strong differentiation thesis”: the claim that mechanistic and functional understanding involve different epistemic relationships between mind and world.