How can the same voltage and resistance produce a different amount of current?
In this video Ben Eater is explaining the need to apply a signal to a load through a driver (a transistor in his example.)
The upper signal is provided by a source that has a high internal output resistor. The lower signal is provided by a power supply with a low output resistor (the output voltage is regulated so we may assume an adaptable output resistor.)
So you must consider the internal resistor like in the following:



simulate this circuit &ndash; Schematic created using CircuitLab
R1 is the internal resistor of the source applied to the upper circuit. R2 is the internal resistor of the power supply applied to the lower circuit (assumed null.)