Steady-State DC Analysis: Inductors and voltage sources
For capacitor ic(t)=C *dvc(t)/dt, when switch is closed there is voltage difference between the +ve and -ve terminal. Hence, there will be flow of current until cap is charged. Since battery is a constant voltage source, the cap will be charged to 10 V and after that there won't be any flow of DC current through it and it will act as open circuit for DC current.

In case of inductor, vl(t)=L *dil(t)/dt, vl(t) is the voltage across the inductor, hence when circuit is closed there is huge di/dt in transisent state and inductor will act as huge resistor. But as the current becomes constant at steady state, di/dt = 0, V(l) = 0 which means voltage across inductor is zero hence short.

The reason for calling the source as voltage source is that it provides constant voltage for different loads which may draw different current.