In this work, a detailed study on the multiplicity characteristics of fast and slow target protons produced in the interactions of 3.3A[Formula: see text]GeV [Formula: see text] and 3.7A[Formula: see text]GeV [Formula: see text]Mg projectiles with the heavy emulsion nuclei (AgBr) is performed. The experimental data of the multiplicity distributions (MDs) of gray (fast protons) and black (slow protons) particles are fitted with the negative binomial and Gaussian distributions indicating a reasonable consensus with each. The validity of scaling hypothesis of MDs of gray and black particles is verified by studying two types of scaling functions, Koba–Nielson–Olsen (KNO) scaling and Hegyi scaling. The experimental data are displayed by a simplified universal function in each scaling. An examination of the relationship between the entropy and the average multiplicity is performed. The measurements of the higher-order moments (mean, variance, skewedness and kurtosis) of MDs of proton target fragments are measured. The second Muller moments are calculated as well to investigate the correlation among the fast and slow target protons.