Plug-in electric vehicles are the currently favoured option to decarbonize the passenger car sector. However, a decarbonisation is only possible with electricity from renewable energies and plug-in electric vehicles might cause peak loads if they started to charge at the same time. Both of these issues could be solved with coordinated load shifting (demand response). Previous studies analysed this research question by focusing on private vehicles with domestic and work charging infrastructure. This study additionally includes the important early adopter group of commercial fleet vehicles and reflects the impact of domestic, commercial, work, and public charging. For this purpose, two models are combined that capture the market diffusion of electric vehicles and their charging behaviour (ALADIN), as well as the load shifting potential of several new energy technologies (eLOAD). In a comparison of three different scenarios, we find that the charging of commercial vehicles does not inflict evening load peaks in the same magnitude as purely domestic charging of private cars does. Also, for private cars, charging at work occurs during the day and may reduce the necessity of load shifting while public charging plays a less important role in total charging demand as well as load shifting potential. Nonetheless, demand response reduces the system load by about 2.2 GW or 2.8% when domestic and work charging are considered when compared to a scenario with only domestic charging where a new peak might be created in the winter hours due to load shifting into the night.