Not that I know. Sometimes the sensors are named and then the definition change (e.g. Advanced Very High Resolution Radiometer would not be called VHR anymore, but it was in 1978)
Your definition is quite practical but does not tell you what you have between the two ranges (e.g. 15 bands like MERIS, Rapideye red Edge is 40 nm... I would put those two in the mlti-spectral category, but as you can see this is out of range).
That being said, I would not rely too much on the number of bands for a definition of hyperspectral. What is more important to me is the method of acquisition. See the difference between radiometer (for multispectral) and spectrometer (for hyperspectral) below:
Radiometers. Radiometers are used to measure the amount of
electromagnetic energy present within a specific wavelength range. The
measurement is expressed in Watts (W) which is a unit of measurement
for power. Radiometers are usually used to detect and measure the
amount of energy outside the visible light spectrum and are used to
measure ultraviolet (UV) light or infrared (IR). A typical use for a
UV meter is in the museum lighting world where the presence of UV is
can be very troublesome. UV energy hastens the ageing process due to
its higher energy content so any energy below 400nm needs to be
filtered out or eliminated. Another application for a radiometer is in
the detection and measurement of infrared or IR. It is used to detect
and measure heat on a surface. Technicians use them to safely detect
and repair overheating motors or shorted out wiring. Radiometers can
measure very quickly because they are simple meters that use only one
sensor with a filter designed to just measure the wavelength range
they were intended for.
Spectrometers. Spectrometers, like radiometers, are instruments that
are also used to measure a specific wavelength range. The biggest
difference is spectrometers use an optical grating or prism and
multiple sensors to break down the incoming energy into different
wavelengths or components. Spectrometers are not complete instruments
and need to be paired with optics in order to work correctly. It can
be used with a camera system to measure watts per square meter SR nm (
W / m2*SR*nm ) or with a cosine corrected head to measure irradiance
and report watts per square meter nm ( W / m2 * nm ). Spectrometers
can have up to 2048 sensors so they are highly analytical and can give
very precise data and can measure very accurately. And since they are
not complete systems, they can be adapted and used in multiple
industries and applications.
So the bandwidth with a radiometer is fixed for a given purpose, while the spectrometer potentially provides a continuous spectrum.