Apologies if I butchered the question, I wasn't quite sure how to word it.
In the Ramakrishnan text (2nd edition) on page 423 (in the section on functional dependencies) this statement is made:
If $X \rightarrow Y$ holds, where [$X$ is the set of key attributes and] $Y$ is the set of all attributes, and there is some subset $V$ of $X$ such that $V \rightarrow Y$ holds, then $X$ is a superkey; if $V$ is a strict subset of $X$, then $X$ is not a key.
I got the basic idea here (that if $X$ contains some $V$ where $V \rightarrow Y$ then $X$ is a key that contains a smaller key), but I must be misunderstanding something on the second case. Why isn't $X$ a key in the second case? It would seem that a strict subset would be a stronger case for being a "key within a key" which is how I understand a superkey to be structured.