Shared peaks count is the simplest imaginable notion of mass spectrum similarity. Given two mass spectra, this metric counts the total number of peaks shared by the two spectra. The analogue of shared peaks count for simplified spectra is a count of the number of masses shared by the two spectra.
The shared peaks count is simple but does not often help us identify similar proteins. For example, if one of our spectra derives from a peptide that is found within the peptide that produces the second spectrum, then the peptides are structurally similar, but the shared peaks count will be relatively small. In fact, the graph of one spectrum will appear shifted with respect to the other spectrum. In this case, we need to identify this shift value in order to quantify the similarity of the two peptides.