Otoacoustic emissions (OAEs) of all types are widely assumed to arise by a common mechanism: nonlinear electromechanical distortion within the cochlea. In this view, both stimulus-frequency (SFOAEs) and distortion-product emissions (DPOAEs) arise because nonlinearities in the mechanics act as "sources" of backward-traveling waves. This unified picture is tested by analyzing measurements of emission phase using a simple phenomenological description of the nonlinear re-emission process. The analysis framework is independent of the detailed form of the emission sources and the nonlinearities that produce them. The analysis demonstrates that the common assumption that SFOAEs originate by nonlinear distortion requires that SFOAE phase be essentially independent of frequency, in striking contradiction with experiment. This contradiction implies that evoked otoacoustic emissions arise by two fundamentally different mechanisms within the cochlea. These two mechanisms (linear reflection versus nonlinear distortion) are described and two broad classes of emissions--reflection-source and distortion-source emissions--are distinguished based on the mechanisms of their generation. The implications of this OAE taxonomy for the measurement, interpretation, and clinical use of otoacoustic emissions as noninvasive probes of cochlear function are discussed.