Curves can be saved on disk for subsequent loading, allowing for comparison between mixes, comparison to a reference spectra, etc.

A snapshot contains the state of the curves at the time it was taken:

A snapshot, as implied by the name, is like a picture of the whole application at a given time. A snapshot contains all the data to save the current signal analysis as displayed on screen, and restore it at any given time, as well as to make comparisons between different locations, setups, etc.