Typically, any connected subgraph of a graph $G$ is called a component of $G$. More specific are those subgraphs of a graph $G$ that are both connected and node-induced.
In areas of applied mathematics, I have come across different terms for the latter. In machine learning research, they are called clusters. In image analysis research, they are called segments. Personally, I prefer to call connected subgraphs just connected subgraphs, and to use the term component for every subgraph that is node-induced and connected. This way, a decomposition of a graph $G = (V,E)$ can be defined as a partition $\Pi$ of the node set such that, for every $V' \in \Pi$, the subgraph of $G$ induced by $V'$ is connected (and hence a component of $G$). However, my using the term this way sometimes causes confusion.
Although I am fully aware that terms are not essential, ultimately, I would like to avoid confusion. Thus, my question is which others terms are typically used for the subgraphs that are both node-induced and connected.