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Photoevaporation driven by hydrogen-ionizing extreme-ultraviolet (EUV) radiation profoundly shapes the lives of diverse astrophysical objects. We construct an analytical model accounting for the finite timescales of photoheating and photoionization and apply it to the dispersal of protoplanetary disks. The model yields improved estimates for the ionization, temperature, and velocity versus distance from the central source when compared to the classical picture of fully ionized and isothermal winds with temperatures ≈10 ^4 K and speeds ≈10 km s ^−1 . In contrast to the classical picture, the photoevaporative winds take on several distinct hydrodynamical and thermochemical states depending on the central star’s EUV emission rate and spectral hardness: T Tauri stars with EUV luminosities around 10 ^30 erg s ^−1 drive nonisothermal ionized disk winds at lower temperatures than the classical value if the spectrum is soft, with an average deposited energy per photoionization less than about 3.7 eV. If, however, the spectrum is hard, the winds tend to be atomic and isothermal at most disk radii. For lower EUV intensities, even with soft spectra, atomic winds can emerge beyond ∼10 au through advection. We show that these predictions are in general agreement with detailed radiation hydrodynamics calculations. The model furthermore illustrates how the energy efficiency of photoevaporation varies with the intensity and spectral hardness of the EUV illumination, as well as addressing discrepancies in the literature around the effectiveness of X-ray photoevaporation. The findings highlight the importance of the photoheating and photoionization timescales both for modeling and for understanding winds’ observed behavior.