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, ie the spin-dependent Seebeck effect. We show that the ratio between magnonic and electronic contribution scales as, with the Fermi temperature T F and the Curie temperature T C. Since, typically,, the magnonic contribution may dominate the thermal spin injection, even though the interface is more transparent for electronic spin current.