In this article, two flexible classes called the modified Kavya–Manoharan-G (MKM-G) and discrete modified Kavya–Manoharan-G (DMKM-G) families are investigated. The two proposed families provide more flexibility for modeling real-lifetime and count data from environmental, medical, engineering, and educational fields. Due to the new extra shape parameter of the two proposed families, their special sub-models are capable of modeling monotonic and non-monotonic hazard rates. The basic properties of the MKM-G family are studied. Eight classical approaches of estimation are used for estimating the MKM-exponential (MKME) parameters. The performances of the estimators are explored using simulation results. Additionally, the DMKM-exponential (DMKME) distribution is defined. Finally, the importance and flexibility of the MKME and DMKME distributions are addressed by fitting seven real-lifetime and count data from aforementioned applied fields. The real data analysis shows that the special models of the two classes are good candidates and can provide close fit as compared to well-known competing continuous and discrete distributions.