Brad,
No this is not entirely correct. Unless you are referring to a lab-based image spectrometer (does collect a continuous spectrum), these terms merely refer to multispectral and hyperspectrial sensors, which are the more common terminologies. Hyperspectrial is not continuous, it just has narrow spectral ranges compared to multispectral sensors. This in combination with a very large number of bands, allows for much higher spectral resolution. But keep in mind that there is also quite a bit more noise and the SNR (signal to noise ratio) can make classification more challenging than with multispectral data.
It is critical that you atmospherically correct hyperspectrial data to remove noise attributed to water vapor and scattering. This is not trivial and requires special software (i.e., MODTRAN, ATCOR, ACORN, FLAASH). Whereas, atmospheric correction of multispectral data is considerabley easier with existing models available in both ERDAS and ENVI.
When hyperspectrial data is brought up as a suggestion in a project, I always ask if the question at hand really supports the processing overhead and expense. Rarely is this is the case and usually multispectral is more than adequate, especially given the increasing spatial resolution of many multispectral sensors. If you have a difficult to detect target or one occurring below the pixel level and want to apply a spectral unmixing approach, hyperspectrial may be a good choice.