What is the term for the unstated elements within rhetoric and/or their use?
An argument with an unstated but implied premise is an enthymeme.
From the Silva Rhetoricae:
Enthymeme
- The informal method of reasoning typical of rhetorical discourse. The enthymeme is sometimes defined as a "truncated syllogism" since either the major or minor premise found in that more formal method of reasoning is left implied. The enthymeme typically occurs as a conclusion coupled with a reason. When several enthymemes are linked together, this becomes sorites.
The implicit premise itself doesn't have a dedicated term which I'm aware of, but you might call it a enthymemetic premise or a suppressed premise or even a tacit premise (as opposed to an explicit premise).
These are the kinds of premises embedded, but hidden, in loaded questions (in fact, they are the very thing the question is loaded with!).