A single-photon avalanche diode (SPAD) is a photon-counting sensor renowned for its exceptional single-photon sensitivity. One significant feature of SPADs is their non-linear response to light, making them ideal for high-dynamic range imaging applications. In SPAD imaging, the photon detection mode, which depends on the quenching method employed, is crucial for optimizing image quality and dynamic range. This paper examines the free-running and gating imaging modes, evaluating their impacts on photon capture and saturation limits. Given that the number of incident photons follows a Poisson distribution, we introduce an innovative imaging-quenching model based on statistical mathematics. We designed and fabricated two SPAD imaging sensors using 180 nm CMOS technology. Image processing and evaluation were conducted using a mapping method. Our results show that in low-light conditions, the gating mode surpasses the free-running mode in the signal-to-noise ratio (SNR). However, the free-running mode exhibits a saturation limit of more than an order of magnitude higher than that of the gating mode, demonstrating its superior capability to handle a broader range of light intensities. This paper provides a thorough analysis of the differences between the two imaging methods, incorporating the theoretical mathematical model, circuit characteristics, and computed imaging quality.