Digital twins of manufacturing systems have become increasingly relevant for use cases such as virtual commissioning and AI related process optimizations such as predictive maintenance or condition monitoring. However, the lack of standardization with regard to implementation tools and the ambiguous use of the term prevent digital twins from widespread industrial application of digital twins. This paper presents a conceptual approach and a successful implementation guide for a digital twin of a modular manufacturing system. First, different notions of the term digital twin from the vast literature are summarized and a unifying definition is presented. Turning to the application example, the modular design of the manufacturing system considered in this paper is outlined as well as the workflow of the industrial assembly process. In the main section a detailed architectural concept for a digital twin of manufacturing systems is presented. Finally, the toolchain that implements this architecture is described emphasizing the functionalities of the components used. The results are discussed and an outlook towards a bidirectionally interdependent digital twin is given.