We have solved the long-standing problem of the mechanism of terahertz (THz) generation by a two-color filament in air and found that both neutrals and plasma contribute to the radiation. We reveal that the contribution from neutrals by four-wave mixing is much weaker and higher in frequency than the distinctive plasma lower-frequency contribution. The former is in the forward direction while the latter is in a cone and reveals an abrupt down-shift to the plasma frequency. Ring-shaped spatial distributions of the THz radiation are shown to be of universal nature and they occur in both collimated and focusing propagation geometries. Experimental measurements of the frequency-angular spectrum generated by 130-fs laser pulses agree with numerical simulations based on a unidirectional pulse propagation model.