This paper addresses the challenges of event-driven learning in spiking neural networks (SNNs) and proposes two novel algorithms: Spike-Timing-Dependent Event-Driven (STD-ED) and Membrane-Potential-Dependent Event-Driven (MPD-ED). These algorithms leverage precise spike timing and membrane potential, respectively, to enhance learning efficiency. The STD-ED algorithm introduces an Adaptive Firing Threshold-based Integrate-and-Fire (AFT-IF) neuron to address over-sparsity and gradient reversal issues, while the MPD-ED algorithm integrates the AFT mechanism into the Leaky Integrate-and-Fire (LIF) model and uses a masked surrogate gradient function to implement event-driven learning. Extensive experiments on static and neuromorphic datasets demonstrate that the proposed methods outperform existing event-driven approaches by 2.51% and 4.79% on the CIFAR-100 dataset, respectively. Theoretical and hardware validation show a 30-fold reduction in energy consumption compared to time-step-based surrogate gradient methods, highlighting the energy efficiency and practical applicability of the proposed methods.This paper addresses the challenges of event-driven learning in spiking neural networks (SNNs) and proposes two novel algorithms: Spike-Timing-Dependent Event-Driven (STD-ED) and Membrane-Potential-Dependent Event-Driven (MPD-ED). These algorithms leverage precise spike timing and membrane potential, respectively, to enhance learning efficiency. The STD-ED algorithm introduces an Adaptive Firing Threshold-based Integrate-and-Fire (AFT-IF) neuron to address over-sparsity and gradient reversal issues, while the MPD-ED algorithm integrates the AFT mechanism into the Leaky Integrate-and-Fire (LIF) model and uses a masked surrogate gradient function to implement event-driven learning. Extensive experiments on static and neuromorphic datasets demonstrate that the proposed methods outperform existing event-driven approaches by 2.51% and 4.79% on the CIFAR-100 dataset, respectively. Theoretical and hardware validation show a 30-fold reduction in energy consumption compared to time-step-based surrogate gradient methods, highlighting the energy efficiency and practical applicability of the proposed methods.