In this paper, we explore the application of Physics-Informed Neural Networks (PINNs) in parameter identification for continuum models of manufacturing systems. Although these models are invaluable for production planning at the factory level, the reliability of model-based decision-making strategies hinges significantly on accurate parameter estimation. We emphasize the distinct differences between PINNs and conventional parameter identification methods, particularly in terms of parameter sensitivities and uncertainty quantification. Our findings reveal that the PINN-based identification framework results in more significant parameter uncertainties. Consequently, this prompts us to discuss the implications for experimental designs, system identification, and the pivotal role of smart data.