What are the key differences between a spectrograph and a spectrometer, and how do these differences impact their respective functions in analyzing light and measuring spectral data?

Well, darling, a spectrograph is basically a type of spectrometer. Spectrograph focuses on producing images of spectra, while a spectrometer focuses on measuring the intensity of light at different wavelengths. So, in the grand scheme of things, it all boils down to how you want to view or analyze that pretty little rainbow of light.