This study investigates the functional equivalency of various random number generation (RNG) models for the PERT (Program Evaluation and Review Technique)-beta distribution in Monte Carlo project risk simulations. The existing project management literature contains multiple PERT-beta RNG models, which are often used interchangeably under the assumption that they possess a level of functional equivalency. Our study highlights that this assumption may be inaccurate, leading to potential model selection errors when analysts apply a PERT-beta model without a thorough understanding of its unique statistical properties. Our study makes three contributions to the field of project risk simulation. First, we identify seven widely used PERT-beta RNG models prevalent in the project management literature and specialized simulation software (e.g., @Risk and Crystal Ball). Second, we conduct a comparative experiment to characterize the stochastic behaviors of each model. Finally, we propose and test a hypothesis on the functional equivalency of these alternative PERT-beta RNG models, employing both parametric and empirical approaches. Both researchers and practitioners stand to gain from these insights, as they facilitate the prevention of model selection errors and mitigate confusion stemming from latent algorithmic discrepancies among the alternative PERT-beta models.