This work investigated whether fundamental differences emerged between segments of complex movement sequences performed at different instructed speeds. To this end, we tested 5 novices and 1 karate expert as they performed beginner's martial arts routines. We found that if one blindly took these segments and separated them according to the variability of trajectory parameters, one could unambiguously group two classes of movements between the same two space regions: one type that remained quite conserved despite speed changes and another type that changed with speed level. These groups corresponded to functionally different movements (strike segments explicitly directed to a set of goals and spontaneously retracting segments supplementing the goals). The curvature of the goal-directed segments remained quite conserved despite speed changes, yet the supplemental movements spanned families of trajectories with different curvature according to the speed. Likewise, the values of the hand's peak velocity across trials were more variable in supplemental segments, and for each participant, there were different statistical signatures of variability between the two movement classes. This dichotomy between coexisting movement classes of our natural actions calls for a theoretical characterization. The present experimental results strongly suggest that two separate sets of principles may govern these movement classes in complex natural behaviors, since under different dynamics the hand did not describe a unique family of trajectories between the same two points in the 3D space.