Shook swarm vs cut down split

Confused about the difference between cut down and shook swarm splits. Possibly because locals at our club are doing splits that seem like cut down by description, but are calling them "shook swarm". Seems like a shook swarm traditionally involves the old queen on new foundation (as in replacing old or contaminated comb, or for regression) at the old site, while a cut down involves moving the old queen and most brood to free bees from brood rearing and switch them to foraging.
My main question is simulating a natural swarm, as a split, and for frame drawing. Moving the OLD queen to a new location, hiving her on all foundation, and feeding syrup like crazy to maximize wax production is as close to this as I imagine. How to get her bees? It would seem shaking young bees off of brood combs would be the most like a natural swarm. Many of us new-bees assume the old foragers fly off with the queen in a swarm, but I'm thinking young bees with wax making capacity makes more sense. Shouldn't a shook swarm involve shaking bees? just sayin'