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Magnetic skyrmions are swirling magnetic spin structures that could be used to build next-generation memory and logic devices. They can be characterized by a topological charge that describes how the spin winds around the core. The dynamics of skyrmions and antiskyrmions, which have opposite topological charges, are typically described by assuming a rigid core. However, this reduces the set of variables that describe skyrmion motion. Here we theoretically explore the dynamics of skyrmions and antiskyrmions in ultrathin ferromagnetic films and show that current-induced spin-orbit torques can lead to trochoidal motion and skyrmion-antiskyrmion pair generation, which occurs only for either the skyrmion or antiskyrmion, depending on the symmetry of the underlying Dzyaloshinskii-Moriya interaction. Such dynamics are induced by core deformations, leading to a time-dependent helicity that governs the motion of the skyrmion and antiskyrmion core. We compute the dynamical phase diagram through a combination of atomistic spin simulations, reduced-variable modelling and machine learning algorithms. It predicts how spin-orbit torques can control the type of motion and the possibility to generate skyrmion lattices by antiskyrmion seeding.