While numerous gait families have been defined and studied for legged systems traversing level ground (e.g. walking, running, bounding, etc), formal distinctions have yet to be developed for dynamic gaits in the vertical regime. Recognition and understanding of different gait families has clear implications to control strategy, efficiency, and stability. While several climbing robotic systems have been described as achieving 'running' behaviors on vertical surfaces, the question of whether distinct dynamic gaits exist and what differentiates these gaits has not been rigorously explored. In this paper, by applying definitions developed in the horizontal regime to simulation and experimental data, we show evidence of three distinct dynamic climbing gaits families and discuss the implications of these gaits on the development of more advanced climbing robots.