Hyperspectral

Hyperspectral imaging is part of a class of techniques commonly referred to as spectral imaging or spectral analysis. Hyperspectral imaging is related to multispectral imaging. The distinction between hyper- and multi-spectral should not be based on a random or arbitrary "number of bands". A distinction that is based on the type of measurement may be more appropriate.
Multispectral deals with several images at discrete and somewhat narrow bands. The "discrete and somewhat narrow" is what distinguishes multispectral in the visible from color photography. A multispectral sensor may have many bands covering the spectrum from the visible to the longwave infrared. Multispectral images do not produce the "spectrum" of an object. Landsat is an excellent example.
Hyperspectral deals with imaging narrow spectral bands over a contiguous spectral range, and produce the spectra of all pixels in the scene. So a sensor with only 20 bands can also be hyperspectral when it covers the range from 500 to 700 nm with 20 10-nm wide bands. (While a sensor with 20 discrete bands covering the VIS, NIR, SWIR, MWIR, and LWIR would be considered multispectral.)
Ultraspectral could be reserved for interferometer type imaging sensors with a very fine spectral resolution. These sensor often have (but not necessarily) a low spatial resolution of several pixels only, a restriction imposed by the high data rate.