A more technical way to describe the "charge" on the open conductor is that you are seeing capacitive coupling.
If you look at the two wires there is a capacitance between them, just as there is a capacitance between any conductive objects that are locally insulated from each other.
You can draw an equivalent circuit for the open wire by drawing one (small) capacitor between the wire under test and any wire near it (like running in the same raceway or cable) that has line voltage on it. And another (also small, but maybe a bit bigger) capacitor between the wire under test and any grounded metal near it. (such as raceway or EGC and neutral in the same NM.)
With no meter attached at all the voltage is determined by a voltage divider effect of the two capacitances, and using a non-contact tester you will see that full voltage.
If you now attach a voltmeter you are adding a resistance in parallel with the capacitor that is going to ground/neutral.
If the voltmeter looks like a very high resistance it will not affect the voltage divider much. If is it a lower resistance, like an old analog meter, a wiggy, or a newer meter that deliberately shows a low input impedance, the voltage read will be lower or even appear to be zero.
As you turn on and off other circuits that run in the same raceway, you may change to value of the phantom voltage.