Large-volume and uniform atmospheric glow discharges are finding a vast range of processing applications, many of which have been traditionally addressed with the vacuum plasma technology. When excited at kilohertz or above, these atmospheric plasmas operate typically at low current densities below 30 mA/cm2 and often they are perceived to have very similar properties regardless of their operation conditions. Recently a radio-frequency (rf) atmospheric glow discharge was observed at high current density of up to 1 A/cm2, thus suggesting a previously overlooked and potentially different operation regime. Through a computational study of rf atmospheric glow discharges over a wide range of current density, this paper presents evidence of at least two glow modes, namely, the α mode and the γ mode. It is shown that gas ionization in the α mode is volumetric occurring throughout the electrode gap whereas in the γ mode it is dominated by localized events near the boundary between the sheath and the plasma bulk. Secondary electron emission strongly influences gas ionization in the γ mode yet matters little in the α mode. These findings suggest a wider operation range of atmospheric glow plasmas than previously believed. The contrasting dynamic behaviors of the two glow modes highlight both the potential to preferentially match the operation regime of atmospheric glow discharges to the specific requirements of their intended applications and the importance to develop diagnostics strategies appropriate for their operation regimes.