Current difference between pinMode(pin, INPUT_PULLUP) and digitalWrite(pin, HIGH)?
It all depends on the external device. If it has high-impedance inputs,
then it makes no difference. The Arduino itself has high-impedance on
its pins configured as INPUT. If the device draws current from this
signal, then chances are it will draw more current from an OUTOUT
HIGH than from an INPUT_PULLUP. How much more? We cannot say without
knowing the specifics of that device.
If you model the device as a simple resistor to ground (which is almost
certainly overly naive), then the current draw is
I = VCC / (R + Ro)
where R is the value of the resistor and Ro the output
resistance of the Arduino: about 25 Ω for an OUTPUT and
32 kΩ for an INPUT_PULLUP.