Optical wireless communication (OWC) leveraging single-photon avalanche diode (SPAD) arrays offers exceptional sensitivity for photon-starving links. However, the inherent dead time of SPADs critically limits achievable data rates by introducing non-linear photon-counting distortions: blocking loss within a symbol duration and inter-symbol interference (ISI) across durations. This paper proposes a unified analytical framework capturing both distortions across all operational speed regimes for pulse-amplitude modulation (PAM), by establishing comprehensive statistical models for SPAD array receivers. For low and medium-speed systems (symbol duration longer than dead time), we derive exact closed-form expressions for the photon counts probability distribution using renewal theory, explicitly incorporating blocking loss and ISI. For high-speed systems (symbol duration shorter than dead time), we develop a Markov chain model characterizing the steady-state operational states and integrate it with trigger probability to obtain the exact binomial photon counts distribution. Furthermore, we propose low-complexity, near-optimal threshold detection schemes based on these models. This work provides essential theoretical tools for designing and optimizing high-performance SPAD-based OWC systems employing PAM.