Future Unmanned Aerial Vehicles (UAVs) are projected to fly and operate in swarms. The swarm metaphor makes explicit and implicit mappings regarding system architecture and human interaction to aspects of natural systems, such as bee societies. Compared to the metaphor of a team, swarming agents as individuals are less capable, more expendable, and more limited in terms of communication and coordination. Given their different features and limitations, the two metaphors could be useful in different scenarios. We also discuss a choir metaphor and illustrate how it can give rise to different design concepts. We conclude that designers and engineers should be mindful of the metaphors they use because they influence—and limit—how to think about and design for multi-UAV systems. © 2021, The Author(s)