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The amount of current through the circuit, and the amount of current you can draw from VOut - apply ohms law and you will see how small the current capability is from a simple resistive divider.
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.
As a rule-of-thumb, you could use resistors with a value chosen such that the current through them is, say, an order of magnitude greater then the input bias current requirement of the opamp.
The difference is the effect a load will have on the desired voltage output. The voltage output will change based on the current drawn by the load. If you have a spare opamp, use it as a non-inverting buffer and buffer the voltage divider output.
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