The difference is the impedance of the bias point; how much the voltage will be affected by current in or out of that point.
If it were eg. feeding just the non inverting input of a CMOS opamp, the resistors could be very high.
If it were acting as a mid supply reference for a circuit with multiple connections and signal currents going back to that point, you would need low value resistors, in proportion to any connected to it.
It would also normally have a capacitor to negative supply, to bypass AC signals and stabilise it.