Good answer Thirdeye. Just to throw some salt on the wound (get it?), to me a cure of any kind involves heavy amounts of "salt" where "salt" can mean table salt (sodium chloride), as well as other salts: Sodium Nitrite, Sodium Nitrate, Potassium Nitrite, and Potassium Nitrate are a few of the more common ones. A cure will also usually includea sugar. The key here is that the salts are used to inhibit bacterial growth, and thus applied for a long period of time (days to weeks to months).
A "rub," to me differs from a cure more than any other way in that it is not intended to inhibit bacterial growth. It may have salt and sugar, but usually not as much, and the meat does not spend as much time in it.
As an asside, consider Lox and other cured salmon products which are cured wtih just NaCl and sugar, no Nitrite/Nitrate in there.
Consider also a pickling solution which is intended to inhibit bacterial growth, but differently. While cures rely on the salts doing that, pickling solutions use an acid, usually acedic acid (vinegar) to do that work. It gets all the more complicated in that when it's all said and done, the nitrites in some cures break down into nitric acid, whereas the NaCl in Sauerkraut breaks down into lactic acid...no vinegar added. Consider also that a "salt" could include Sodium DiAcetate, which will break down into Acetic Acid (vinegar). Again, the differences between these things can be debated on several levels...but if there is not NaCl disolved in solution by HOH, it definitely is not a brine....
dmp