Murmurations along with other forms of flocking have come to epitomize collective animal movements. Most studies into these stunning aerial displays have aimed to understand how coherent motion may emerge from simple behavioral rules and behavioral correlations. These studies may now need revision because recently it has been shown that flocking birds, like swarming insects, behave on the average as if they are trapped in elastic potential wells. Here I show, somewhat paradoxically, how coherent motion can be generated by variations in the intensity of multiplicative noise which causes the shape of a potential well to change, thereby shifting the positions and strengths of centres of attraction. Each bird, irrespective of its position in the flock will respond in a similar way to such changes, giving the impression that the flock behaves as one, and typically resulting in scale-free correlations. I thereby show how correlations can be an emergent property of noisy, confining potential wells. I also show how such wells can lead to high density borders, a characteristic of flocks, and I show how they can account for the complex patterns of collective escape patterns of starling flocks under predation. I suggest swarming and flocking do not constitute two distinctly different kinds of collective behavior but rather that insects are residing in relatively stable potential wells whilst birds are residing in unstable potential wells. It is shown how, dependent upon individual perceptual capabilities, bird flocks can be poised at criticality.