ABSTRACT This work examines the relationships between the properties (flux ratios, full width at half-maximum velocities) of the O i λλ6300, 6364, Ca ii λλ7291, 7323, and the Ca ii near-infrared triplet, emission lines of a large sample of core-collapse supernovas (SNe) and Ca-rich transients (509 spectra of 86 transients, of which 10 transients are Ca-rich events). Line-flux ratios as a function of time were investigated with differences identified between the transient classes, in particular the Type II SNe were found to have distinct line-flux ratios compared to stripped-envelope (SE) SNe. No correlation was found between the Ca ii/O i flux ratios of SE-SNe and their ejecta masses and kinetic energies (as measured from light-curve modelling), suggesting that there may be a contribution from an additional power source in more luminous SE-SNe. We found that the mean characteristic width of the Ca ii emission line is less than the O i emission line for all SN types, indicating that the Ca ii emission typically originates from deeper in the ejecta than O i. This is in some tension with standard models for emission in Type II SNe. The emission line properties of Type II SNe were also compared to theoretical models and found to favour lower mass tracks (MZAMS< 15 M⊙), with no evidence found for significant mixing of 56Ni into the H envelope nor Ca mixed into the O shell. The flux ratios of some superluminous SNe were found to be similar to those of SE-SNe when scaling to account for their longer rise times was applied (although we caution the sample size is small).