In the field of systems-of-systems (SoS) engineering, there is broad agreement on a few characterizations, and these are currently being standardized. However, many aspects in the field still lack an established terminology. In particular, there are unclarities related to the internal structure of an SoS, and on the internal states of constituent systems. In this paper, a refined terminology is therefore proposed, which covers the internal substructure of an SoS; the states of constituent systems in relation to those substructures; and how it relates to hierarchical levels. This terminology can also be used to classify the characteristics of an SoS through different metrics. The terminology is illustrated through three examples of SoS applications in various domains. © 2019 IEEE.