The radiation hardness of 180 nm complementary metal-oxide-semiconductor (CMOS) and 55 nm bipolar-CMOS-double-diffused MOS single-photon avalanche diodes (SPADs) is studied using 10 MeV and 100 MeV protons up to a displacement damage dose of 1 PeV/g. It is found that the dark count rate (DCR) levels are dependent on the number and the type of defects created. A new stepwise increase in the DCR is presented. Afterpulsing was found to be a significant contributor to the observed DCR increase. A new model for DCR increase prediction is proposed considering afterpulsing. Most of the samples under test retain reasonable DCR levels after irradiation, showing high tolerance to ionizing and displacement damage caused by protons. Following irradiation, self-healing was observed at room temperature. Furthermore, high-temperature annealing shows potential for accelerating recovery. Overall, the results show the suitability of SPADs as optical detectors for long-term space missions or as detectors for high-energy particles.