Simulated room impulse responses (RIRs), often generated via the image source method (ISM), are widely used in audio signal processing as scalable alternatives to resource-intensive measurements. However, a systematic acoustic and perceptual gap persists between simulated and measured RIRs, mainly due to phenomena such as diffraction, scattering, and device-specific influences that most geometric simulators neglect. Moreover, no automated tool exists to distinguish these RIRs. We introduce RIR-SoM (RIR Simulated-or-Measured), a compact residual network that classifies RIR waveforms via discriminative embeddings. Trained on measured and ISM-generated RIRs, RIR-SoM is evaluated on unseen rooms and unseen simulation methods, including different ISM reflection orders, a wave-based simulator, and device response augmentation. RIR-SoM separates ISM-simulated from measured RIRs almost perfectly, with progressively lower separability for other held-out datasets. An embedding analysis shows that simulated and measured datasets occupy distinct regions of the learned representation, and a saliency analysis localizes the temporal regions associated with measured-label decisions.