We develop a theory for spin transport in magnetic metals that treats the contribution of magnons and electrons on equal footing. As an application, we consider thermally-driven spin injection across an interface between a magnetic metal and a normal metal, i.e. the spin-dependent Seebeck effect. We show that the ratio between magnonic and electronic contribution scales as √ T/T/c F/Tc, with the Fermi temperature TF and the Curie temperature TC. Since, typically, TC≪ TF, the magnonic contribution may dominate the thermal spin injection, even though the interface is more transparent for electronic spin current.