Swarm describes a behaviour of an aggregate of animals of similar size and body orientation, often moving en masse in the same direction. "Swarming" is a general term that can be applied to any animal that swarms. The term can be applied to insects, birds, fish, various microorganisms such as bacteria, and people. The term applies particularly to insects. "Flocking" is the term usually used for swarming behaviour in birds, while "shoaling" or "schooling" refers to swarming behaviour in fish.
Swarm is the social confluence of similarity. On a human level, it happens when we pay attention to the myths that connect us. That's why, as I suggest in The Stories That Connect Us, it matters what stories we share. Our choice of stories create either the fermentations of swarms or fragmentations of isolation.
Only certain kinds of stories have the power to provoke swarms. Think about what those could be, propagate them, and watch a swarm emerge!