Current limiting resistors and voltage dividers

I answered this SE EE question yesterday.

My answer

OP said: ... current and voltage is like a water in a river...

Analogies

General. There are many examples in life where a pressure-like quantity (voltage) controls a flow-like quantity (current) through an impedement-like quantity (resistance).

"Fish-tank". This is maybe the best water analogy where the pump pressure controls the water flow by overcoming the valve obstructions in the pipeline.

"Communicating vessels". This is another famous water analogy similar to your "river analogy". Here, the voltage is represented by a water column of proportional height. I have used this analogy in a stylized form (segments in red) to visualize the voltages in the pictures below; currents are visualized by loops in green.

Circuit evolution

OP said: ... my confusion is when it comes to current limiting and voltage dividers.

These circuit configurations are closely related and exist together in circuits. I will show their evolution with a step-by-step scenario that I have used in my classes with students:

1. "Ideal" voltage source. Your 5 V voltage source is a typical example of such a device. Whatever load (resistance RL) you connect to it, its voltage will always be 5V.

2. Real voltage source (unloaded). Now connect a resistor Ri in series and an "ideal" voltmeter after the resistor. To our surprise, the voltmeter shows 5 V again. Why? The explanation is that although there is a resistance included in the circuit, there is no voltage drop across it because there is no current (open circuit). As a result, the voltage after Ri is the same as the voltage before Ri.

3. Real voltage source (loaded). Now connect a load RL after Ri. The circuit is closed and current I = V/(Ri + RL) flows. There is a voltage drop across Ri and the output voltage across the load is decreased - VL = V.RL/(Ri + RL). In some cases this is undesirable...

4. Voltage divider (unloaded). ... but in others it is desirable because this is the way to reduce a voltage. Thus the voltage divider was invented where the total resistance Ri + RL determines the current and RL determines the output voltage. So the load resistance RL and the source resistance Ri constitute a voltage divider where the role of the second resistor RL is to cause a current to flow and a voltage drop to appear across Ri.

5. Voltage divider (loaded). When the load has a high resistance and we still want to significantly reduce the voltage, we include an additional second resistor R2 in parallel to increase the current.

6. Current-limiting resistor. But if we go too far and connect a load with a very low resistance (for example, in the case of a short-circuit RL = 0), the current will be determined only by Ri. This resistor then works as a "voltage-to-current converter" or, more simply, as a "current-limiting resistor". This is the simplest way to make a current source. I think this answers the OP's last question.