Stochastic-growth theory (SGT) of bursty waves is generalized and it is shown that the previously separate theory of "elementary bursts" is a limiting case. New regimes of SG are found and elucidated, and results are compared with the first relevant simulations via quasilinear theory and a reduced-parameter model. Both display stochastic behavior with the expected properties--the first simulations to demonstrate SGT behavior explicitly. Reexamination of data and simulations previously analyzed using SGT or elementary burst theory also shows good agreement with the new predictions.