Every verbal or nonverbal encounter has at its core human essence. So, rhetoric analysis (RA) focuses and applies principles from human based analytical tools to examine interactions between interlocutors in different communicative settings.
Rhetorical discourse analysis (RDA) is wider in scope and all encompassing than (RA). It synthesizes different theoretical methods and principles like Classical Rhetoric theory, discourse analysis, cultural theory and rhetoric theory in its inquiry into all elements of rhetorical situations.
In my view these are no standardized, key terms. I tend to say: rhetorical discourse analysis is rhetorical analysis applied on discourse, while rhetorical analysis in general may also apply to other forms of human interaction and even on forms of interaction of a human audience with its environment. Rhetorical analysis in the broad sense is all analysis of how in human interaction one party (an audience) is guided in the way in creates its representation of the world by any act of another party (a rhetor). In my book Gold Mining; the Art of Rhetorical Discourse Analysis (all chapters free downloadable here on Research gate) I try to apply this broad definition on discourse analysis, but depart from how in general humans make sense of their perception of the world surrounding them.