For the differentiator op-amp, what is the difference between active and passive high-pass? Is this just when you input a voltage or no voltage?

A passive high-pass filter is just the simple $CR$ circuit, with no active components. It will have a gain of 1 for high frequencies (high $\omega$ gets through the capacitor) but will attenuate low frequencies. This circuit also acts as a differentiator for (low) frequencies at which the signal is getting attenuated. If the circuit is passive -- no energy added to it -- you always lose signal amplitude in the low-frequency regime.

An active high-pass filter includes an op-amp (or some other amplifying circuit involving transistors). This provides a gain to the input signal. But the active high-pass filter will still attenuate low frequencies (and differentiate) with respect to the nominal gain at high frequencies (and the gain can go below unity).

In both active and passive filter cases you are putting in a signal voltage. But in the active case you are adding energy to the circuit via a power supply (controlled by the op-amp, which has transistors inside), so that the output can have larger amplitude than input.

BTW the same discussion holds for passive low-pass vs active low-pass filters.