Accessing complete information about the emission from any quantum-optical systems requires tools capable of a frequency-resolved characterization of multi-photon transitions that would go beyond the standard g(2) correlation measurements. This is particularly important when analyzing systems which exhibit strong nonlinear response with multiple emission pathways. In this work, we calculate and analyze in details correlations of light emitted from two such canonical nonlinear optical systems, one incorporating Kerr nonlinear medium, and another exhibiting optomechanical coupling between light and quantized motion of a generic mechanical oscillator. We compare their single-and two-photon emission characteristics by employing a recently developed framework that allows us to calculate the frequency-resolved g(2) correlations between emitted photons with two arbitrary frequencies. Our analysis shows a rich landscape of bunching and antibunching associated with multi-photon emission events, and reveals the distinctive temporal characteristics of such processes. This new understanding provides a new asset to characterize and exploit nonlinear phenomena in Kerr and optomechanical systems in future experiments.