The term of art that may help you, which I haven’t seen yet here, is “circumscription”, meaning the boundaries set by a particular author to delimit what does or does not belong to a particular taxon. This has no nomenclatural status; to a first approximation, we are not bound to the text of the original author’s description, but rather to the type associated with the taxon. However, as Keir points out, “sensu” following a scientific name is often used to help dispel ambiguity as to the circumscription being used. The terms “sensu lato” (abbrev. s.l., “in the broad sense”) and “sensu stricto” (abbrev s.s., “in the strict sense”) are often used when a particular name has been used by different authors both to include certain taxa or to exclude them. (You can also break out the superlatives “sensu latissimo” and “sensu strictissimo”, but that’s showing off.)
When you say “not really synonyms” in your first post, taxonomists would usually distinguish between “homotypic synonyms”, where multiple names are based on the same type specimen (but usually have a different rank or genus) and “heterotypic synonyms”, which have a different type from the senior name that an author considers to be of the same taxon. Homotypic synonyms can usually (I’m too tired to talk about replacement names) be identified when their authority is written in full; the parenthetical (G.S.Mill & Standl.) in the two names you cite indicates that both those names are based on Nymphaea ozarkana G.S.Mill & Standl. (In printed synonymies, homotypic synonyms are often listed with a tribar while heterotypic synonyms get an equals sign; I admit this would be a nice feature on POWO.)
All of this is usually expressed in a rather nebulous fashion because circumscriptions are in fact nebulous and do not have completely closed boundaries. More anon.