Considering that it is often subject to various stochastic white noise during the process of integrated pest management, and discrete models are more accurate in describing the situations where the successive generations of many species in nature are non-overlapping and the data of biological samples are usually collected in discrete time, this report presents and analyzes two distinct stochastic discrete models to investigate the effects of stochastic white noise on population dynamics. The first model develop a stochastic discrete crop-pest-natural enemy model using the Positive and Elementary Stable Nonstandard method, which preserves the positivity and stability of equilibria from the original continuous system, independent of the time step size. We provide sufficient conditions for the stability in probability of the pest-extinction and positive equilibria. Numerical simulations demonstrate that unlike the Euler method, which diverges with large step sizes, the PESN discretization exhibits numerical stability and better preserves the dynamical properties of the correponding deterministic discrete model. The second model introduces multiplicative white noise, modeled as independent double-truncated standard normal sequences, directly affecting the pest growth rate and natural enemy mortality. For this model, we establish the positivity and boundedness of solutions and derive sufficient conditions for pest extinction. Our analysis reveals that while low-intensity noise does not alter the population's fate, excessively high noise intensity can drive a population to extinction.