Instruments operating at or near visible light typically use prisms or
gratings that angle light according to wavelength (dispersion).
Dispersion with prisms is small so often multiple prisms are used in
tandem, e.g., a triple prism spectrograph.
Photometry is something like an extremely-low-resolution
spectroscopy, studying stars and astronomical bodies based upon
just a few passbands. Its advantage is that it requires much
less EMR, thus can be used for more distant objects, and is also
multi-object by default.
Some spectroscopy instrument terms/classes:
monochromator - isolates and measures intensity of a very narrow band.
spectrometer - measures intensity of the spectrum of incoming EMR by wavelength.
spectroscope - enables observation of the spectrum.
spectrograph - creates a graphical representation of the spectrum. (Note that modern research instruments typically could fall under any of these three and the term used is basically arbitrary).
slitless spectrograph - without the usual slit aperture that other spectrographs use to prevent overlapping of the spectra of different points in the sky.
Intensity at each wavelength is typically the quality of interest
but there are also cases when polarization at each wavelength
is the quality of interest (spectropolarimetry). Other terms
for various branches of spectroscopy:
Note that the same terms are also sometimes used for analogous
analysis of quantities other than EMR-wavelength, perhaps most often
using the word spectrography. Examples are the mass or
kinetic energy of some source of particles (e.g., the term
mass spectrometer).