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Fast radio bursts (FRBs) are millisecond-duration extragalactic radio transients. They fall into the categories of repeaters and apparent nonrepeaters. However, such a classification causes a lack of motivation to investigate the physical picture. Here, we propose a unified geometric model to distinguish between repeaters and apparent nonrepeaters, in which the quasi-tangential (QT) propagation effect within the magnetosphere of a neutron star is considered. In this model, apparent nonrepeaters arise from sources whose emitting region has a smaller impact angle with respect to the magnetic axis, while repeaters come from sources whose emitting region has a larger impact angle. The observational discriminant polarization properties between repeaters and apparent nonrepeaters are an important clue for verifying this unified geometric model since the polarization is sensitive to the QT propagation effect. Moreover, our model effectively explains all of the other discriminant properties, including bandwidth, duration, peak luminosity, energy, brightness temperature, time–frequency downward drifting, and repetition rate, providing compelling evidence for the magnetospheric origin of FRBs.