Classical Poissonian probabilistic seismic hazard assessment (PSHA) relies on the rate of independent mainshocks to estimate future seismic hazard levels. Real earthquakes, however, cluster in time and space. How different is hazard assessed by Poissonian PSHA from that generated by clustered seismicity? In this synthetic study, we simulate short‐ and long‐term catalogs and ground motions using a generic, temporal epidemic‐type aftershock sequences (ETAS) model assuming a single point source in a subduction zone setting, and we compare the ETAS‐simulated hazard with approximations based on the declustered Poisson approach (DP), the nondeclustered Poisson approach (NDP), and the recently proposed sequence‐based PSHA (Iervolino et al., 2014). Our comparisons reveal that the extent to which the approximations are good depends on the probability levels (return periods) of interest: (1) at (low) building design‐oriented probability (i.e., 10% or 2% in 50 yr), the approximate PSHA methods give peak ground acceleration (PGA) estimates to within ± 7% of the ETAS hazard; (2) at high probability level (>∼45% in 50 yr), the methods interestingly overestimate the ETAS hazard, a subtle consequence of the poor Poisson approximation to the skewed ETAS distributions; and (3) none of the approximate methods reproduce the multiple exceedance curves implied by the ETAS model, suggesting that cumulative seismic risk assessment with damage‐dependent fragility curves should account for ETAS‐like sequences. We also investigate the relation between short‐term (conditional) and long‐term hazard, and propose a hazard analog of the Omori–Utsu and Utsu–Seki scaling laws as a function of initial magnitude, elapsed time, and long‐term hazard. This model can provide a quick prediction of ensemble‐averaged short‐term hazard and the time needed for the hazard levels to return to the long‐term average. We conclude that realistic multigenerational earthquake clustering has both obvious and more subtle effects on long‐ and short‐term hazard, and should be considered in refined hazard assessments.