Cooking is the process of attempting to rid the rock of as much PO4 and built up nutrients as possible while establishing a bacterial colony to handle the waste. Curing is just a short term process that establishes the bacteria without worrying about trying to limit/remove PO4 and other nutrients from the rock.
If you have the time/space, cook the dry rock and start with the best rock possible as far as PO4 and bacteria colonies.
when the term curing was first introduced into the hobby, it was pretty synonymous with cooking. which had not been introduced yet. cooking is a very new term, in the last 5 years or so. curing LR has been around for 20+ years, at least as long as i have been in the hobby.
back in the 80's, cured LR was LR that had been sitting in a huge vat for at least a month without any light. this was the stuff you wanted to buy. the new stuff that just came was in the other vat waiting for all of the unwanted critters and algae to die off. then the sand people came along and thought all of those critters were a good thing, so now cured LR was not what people wanted. now we find that we do not want all of the stuff that tends to grow on the fresh LR and we now call it cooking/purging.
i know way to much info, but good to know the history.