In contrast to other primates, human children's imitation performance goes from low to high fidelity soon after infancy. Are such changes associated with the development of other forms of learning? We addressed this question by testing 215 children (26-59 months) on two social conditions (imitation, emulation)--involving a demonstration--and two asocial conditions (trial-and-error, recall)--involving individual learning--using two touchscreen tasks. The tasks required responding to either three "different" pictures in a specific "picture" order (Cognitive: Airplane?Ball?Cow) or three "identical" pictures in a specific "spatial" order (Motor-Spatial: Up?Down?Right). There were age-related improvements across all conditions and imitation, emulation and recall performance were significantly better than trial-and-error learning. Generalized linear models demonstrated that motor-spatial imitation fidelity was associated with age and motor-spatial emulation performance, but cognitive imitation fidelity was only associated with age. While this study provides evidence for multiple imitation mechanisms, the development of one of those mechanisms--motor-spatial imitation--may be bootstrapped by the development of another social learning skill--motor-spatial emulation. Together, these findings provide important clues about the development of imitation, which is arguably a distinctive feature of the human species.