What is the difference between a forest and a spanning forest?

So suppose I have three disjoint sets of vertices: $\{v_{1}\} \cup \{v_{2}\} \cup V(C_{3})$. Here, $\{v_{1} \} \cup \{v_{2}\}$ is a forest which does not span, while $\{v_{1}\} \cup \{v_{2}\} \cup (C_{3} - e)$ is a spanning forest, for $e \in E(C_{3})$.