Photon and dark avalanche signals of InGaAs single-photon avalanche diodes (SPAD) are detected and counted indiscriminately, while their specific characteristics are not well understood, which hinders further performance optimization of InGaAs SPAD. Here, we investigate back-incidence InGaAs SPAD operating at room temperature by designing a dual-threshold discriminator and tuning the threshold voltage. The photon count rate and dark count rates (DCR) exhibit different abrupt-voltage variations with the threshold voltage, and the amplitude distribution of dark avalanche signals is more concentrated and slightly larger than that of photon avalanche signals. The smaller photon avalanche signals have a faster time response. It can be inferred that the above characteristics are related to the photon absorption position and carrier transport, depending on physical structure and operating mode, and dark counts are mainly caused by holes drifting from N-type material. We use a dual-threshold discriminator to reduce the time jitter and DCR caused by thermally excited carriers. The experimental results are in good agreement with theoretical analysis, indicating that the insertion of an i-InP layer or the use of a front-incidence technique can further optimize the overall performance and enable InGaAs SPAD with high performance operation at room temperature.