interregnum

reg stands for king or kingly styles (e.g. in regicide,regalia etc.) so inter regnum = in between two kings(referring to their ruling period).

Inter(Interval)+Regnum (Kingship)-->Interval between kingship, government etc.

inter + regime

he interval between two reigns; any period when a state is left without a ruler

period of no (inter)fering (reg)ime