Electrical spin injection into semiconductors paves the way for exploring new phenomena in the area of spin physics and new generations of spintronic devices. However the exact role of interface states in spin injection mechanism from a magnetic tunnel junction into a semiconductor is still under debate. In this letter, we demonstrate a clear transition from spin accumulation into interface states to spin injection in the conduction band of $n$-Ge. We observe spin signal amplification at low temperature due to spin accumulation into interface states followed by a clear transition towards spin injection in the conduction band from 200 K up to room temperature. In this regime, the spin signal is reduced down to a value compatible with spin diffusion model. More interestingly, we demonstrate in this regime a significant modulation of the spin signal by spin pumping generated by ferromagnetic resonance and also by applying a back-gate voltage which are clear manifestations of spin current and accumulation in the germanium conduction band.