Current Slowdown: The inductor ($L$) opposes changes in current via self-inductance (Lenz's Law). The higher the inductance ($L$), the more resilience the circuit has to changes in current. When an EMF ($E$) is applied, the changing magnetic flux induces a Back EMF that resists the flow, causing current to ramp up gradually.
Resistive Scattering: In the resistor, moving electrons collide with the ion lattice. When there is no current, the carriers are not being driven through the lattice. This friction limits the final steady-state current to $I = E/R$.