This study proposes random-parameters multinomial logit models, with heterogeneity in means and variances, to explore the differences in the factors influencing injury severities of drivers involved in different types of two-vehicle crashes. The models are verified using crash data from the United Kingdom (UK) over three years (2016–2018). Three types of crashes are separately identified (car-car, car-truck, and truck-truck crashes). In this study, a wide variety of potential variables, including the driver, vehicle, road, and environmental characteristics, are considered, with two possible injury-severity outcomes: severe and slight injury. The results show that unobserved heterogeneity existed for young drivers in both car-car and truck-truck crash models and the 30 mph speed limit in the three separate models. Remarkably variations are observed in crashes involving different types of vehicles. The driver’s age and gender, speeding, sideswipes, presence of junctions, weekdays, unlit, and weather conditions significantly impact driver-injury severities in various types of vehicle crashes. These findings are expected to help policymakers seek to improve highway safety and implement proper safety countermeasures.