Abstract El Niño–Southern Oscillation (ENSO) is the leading mode of climate interannual variability, with large socioeconomical and environmental impacts, potentially increasing with climate change. Improving its understanding may shed further light on its predictability. Here we revisit the two main conceptual models for explaining ENSO cyclic nature, namely, the recharge oscillator (RO) and the advective–reflective delayed oscillator (DO). Some previous studies have argued that these two models capture similar physical processes. Yet, we show here that they actually capture two distinct roles of ocean wave dynamics in ENSO’s temperature tendency equation, using observations, reanalyses, and Climate Model Intercomparison Project (CMIP) models. The slow recharge/discharge process mostly influences central-eastern Pacific by favoring warmer equatorial undercurrent and equatorial upwelling, while the 6-month delayed advective–reflective feedback process dominates in the western-central Pacific. We thus propose a hybrid recharge delayed oscillator (RDO) that combines these two distinct processes into one conceptual model, more realistic than the RO or DO alone. The RDO eigenvalues (frequency and growth rate) are highly sensitive to the relative strengths of the recharge/discharge and delayed negative feedbacks, which have distinct dependencies to mean state. Combining these two feedbacks explains most of ENSO frequency diversity among models. Thanks to the two different spatial patterns involved, the RDO can even capture ENSO spatiotemporal diversity and complexity. We also develop a fully nonlinear and seasonal RDO, even more robust and realistic, investigating each nonlinear term. The great RDO sensitivity may explain the observed and simulated richness in ENSO’s characteristics and predictability. Significance Statement El Niño and La Niña events, and the related Southern Oscillation, cause the largest year-to-year variations of Earth’s climate. Yet the theories behind them are still debated, with two main conceptual models being the recharge oscillator and the delayed oscillator. Our purpose here is to address this debate by developing a more realistic theory, a hybrid recharge delayed oscillator. We show how simple yet realistic it is, with equivalent contributions from the slow recharge process and from the faster delayed feedback. It even captures the observed El Niño and La Niña diversity in space and in frequency. Future studies could use the simple theoretical framework provided here to investigate El Niño–Southern Oscillation (ENSO) in observations, theories, climate models diagnostics and forecasts, and global warming projections.