Confused about Electrical Resistance?

You have to look at the whole circuit. A potential divider or as we call it in the US, a voltage divider "slices" off a piece of the voltage resulting from current through resistors. Suppose you have a 12v source and you have a 6v light bulb. If you know the amps the bulb draws at 6v, you place that bulb in series with a resistor that will drop 6 volts with those amps through it. That way voltage across the bulb will be 12-6=6v. If the pd you are using consists of 2 resistors with the "load" connected off one of the resistors, that load in parallel with that resistor could decrease the equivalent resistance, increasing the current in the circuit which would then drop more voltage across the other resistor, lowering the voltage to the load. Ideally the load connected across the resistor draws negligible current with little variation so that the voltage across the load is fairly constant. If that is not the case, if the load draws significant current or widely varying current, a voltage regulator tab will have to used with sufficient heat sinking. Regarding the last statement, again it depends on the circuit. There are likely other resistors connected in series or in parallel. In a circuit with a single resistor across a voltage source, that statement would be true but it isn't true in a circuit with other resistors.