I have never worked with NAH but guessing from the above, one obvious difference would be that exterior NAH ignores reflections, i.e. has absorbing boundary conditions, while Interior NAH must account for sound that is reflected from interior boundaries.
Usually, this makes Exterior NAH the easier/more reliable methods.
If you are into NAH, I would encourage you to take a look at the MicroFlown. It is a particle velocity measurement probe that overcomes many of the limitations faced with techniques such as sound intensity and NAH as it allows direct measurement of acoustic particle velocity. http://www.microflown.com/
In NAH, you use microphones to acquire sound level on a surface. Then, you use this information to compute the pressure (or velocity, intensity) on another parallel surface. (In mathematical terms, the recording from the microphones acts as a boundary condition to solve the wave equation with the Greens formulation.)
You can either compute the sound level on a surface that is closer to the acoustic source, or that is further away from the source, which corresponds to the "interior" or "exterior" cases when the microphone surface is a sphere.
Because of the amplification of evanescent waves, the "interior" case usually requires additional signal processing.
No. In NAH, you always acquire the sound pressure in the near-field of the source in order to get the evanescent (attenuating) wave component.
With that information, you can compute the sound level at other spatial positions. The position can be closer to the source, or further away from the source.
In my opinion, even in the "exterior" case (further from the source in a spherical system), you would still be in the near-field since the propagation distances are relatively short.
You can read Fourier Acoustics by Williams for more info.
I think that this question is only about terminology. Strictly speaking acoustic holography is not correct combination of words. Before invention of optical holography engineers operating with linear fields (acoustic or radio) perfectly knew how to reconstruct patterns in near field zone or in far fiekd zone, because their sensors are linear. So when optical holography appeared people tried to use these principles tfor acoustics and radio and they understood very fast that it is not necessary to register the intensity of scatterred field with reference wave, as in optical holography because optical sensors are quadratical
Moreover math background. is similar as for holography as for acoustic arrays.
Other story if you want to reproduce classical optical scheme of holography: to register the intensity of sum of scatterrred filed with reference wave and then use Fourier methods or Kirhgoff integral for reconstruction. But having linear acoustic sensors there is no need to do it. The result will be worse.
Interesting comment. You are perfectly right in saying that optical and acoustical holography are not exactly the same, but have similar mathematical basis.
I guess that "acoustical holography" generates more enthusiasm than "Fourier domain sound propagation method", which explains the choice of terminology.