Parental self-efficacy (PSE) is an essential predictor of parenting practices and child development. The content-specificity of PSE is not well understood: Previous studies are based on either measure of general parental self-efficacy or task-specific parental self-efficacy but not measures of both constructs. Thus, we do not know how both constructs are related. With data from the "AQuaFam" study, we compared four-factor models to investigate the structure of PSE. It was a priority whether (1) task-specific and general PSE could be assessed separately or (2) be mapped in a hierarchical model with task-specific PSE factors and a superordinate factor of general PSE. A Chi-square test shows no significant model improvement, which indicates general and task-specific PSE being separate dimensions. US studies suggest that low-income parents, migrants, or parents with a lower educational status experience lower PSE. To adequately support these parents, we need to know whether differences according to families' background characteristics occur in task-specific and general PSE beliefs. We tested general PSE and PSE in four parenting tasks for differences according to families' background characteristics. Parents with a university degree they were self-efficacious in communicating responsible media use than parents without a university degree. Parents with a non-German family language they were self-efficacious in communicating a responsible media use, caring for a sick child, and in their general PSE compared to parents with German as a family language. The results of the group differences are discussed in the context of how to support different parent groups.