We wrote this paper in an attempt to show the way we pass from the results on ordered semigroups based on ideals to the results on semigroups -without order- based on ideals, and conversely. We tried to use sets instead of elements in the proof of our results as an example to show that in the theory of semigroups -without order- based on ideals, elements do not play any role but the sets. Besides, the results of semigroups -without order- based on ideals can be also obtained either by an easy modification of the results on ordered semigroups (by setting $A$ instead of $(A])$ or as an application of the results on ordered semigroups in the way indicated in this paper.