W[1]-hardness of Steiner tree w.r.t. number of non-terminal vertices
When parameterized by number of non-terminal vertices in the input graph, Steiner Tree is FPT by brute force. ​ - ​ Find a minimum-size subset of non-terminal vertices such that [the subgraph induced by the union of [the set of terminal vertices] with [the chosen set of non-terminal vertices]] is connected, and then output any spanning tree of that subgraph.

(If that's not your interpretation of the problem, then clarify your last paragraph.)