I'm used to hearing the terms time domain and frequency domain. But I've never heard pitch domain as a separate idea. Isn't pitch just the same as frequency?
However, the relationship between absolute pitch and frequency isn't always trivial. The latter is a physical phenomenon, but the former is psycho-acoustic. When you have sounds with a normal set of overtones that align with a harmonic series, the perceived pitch matches the fundamental frequency. But that frequency doesn't actually need to be audible. By weighting the amplitudes of the partials in a certain way, you can also construct a sound that will be perceived as different pitches by different listeners, or by the same listener under different circumstances.
With sounds whose frequencies aren't all harmonic, assigning a pitch can get more complicated.
In general I've found the world of music theory to be difficult to penetrate as an outsider, just gotta take small bites.
Not only is it not trivial, it is undefined. For example, "middle C" can map to different frequencies depending on your tuning system, for just one example.
Pitch is the higher level abstraction. Especially on the organ, "middle C" may get interpreted as "middle C plus a C an octave below, plus another octave below for good measure" depending on context. I assume that's what Carpenter is changing when he's putting his hand on those pads where the stops should be.