Generally speaking, the first three words are synonymous. They refer to non-tobacco flavors and/or sweeteners that are added to blends at some point during the manufacturing process. They are the added ingredients that help to make "aromatics" aromatic. And aromatics -- again, generally speaking -- are tobacco blends that are flavored to smell (and, to a lesser degree, taste) like something other than straight tobacco: chocolate, coffee, fruits, berries, vanilla, nougat, etc., etc.
Non-aromatic blends can include very light touches of some of these additions as well. But the flavor/aroma profile is still intended to represent tobacco, not something else. For example, rum is sometimes added to a Virginia/burley flake, but that doesn't mean it's actually an "aromatic" blend. Bob's Chocolate Flake is another flake that includes a light dusting of cocoa; yet I think most folks would still categorize it as a non-aromatic because the overall flavor/aroma is tobacco, not chocolate.
You didn't mention "scented" tobaccos. I put these in the category of non-aromatics, but they include a floral/perfumey scent/flavor that makes them distinctive. These are also commonly known as "Lakeland" blends, because the two main producers of these flakes are based in England's Lake District: Samuel Gawith and Gawith & Hoggarth. Many pipe smokers describe the flavor of Lakelands as "soapy" and either love it or despise it.
Non-aromatic blends are sometimes lumped together as "English" blends. I don't favor that, though, because I personally believe that latakia needs to be present in a blend for it to be called an English. So I think "non-aromatics" is a better way to describe straight Virginias, Virginia/perique blends, and Virginia/oriental blends. But it's a lot easier to just say "English or aromatic" than wrestle with all of the possible nuances.
Again, these are generalities and there are exceptions. And that's probably more than you wanted to know!
Bob