I call them hard boiled. I can finally cook them the right way so they don't turn green around the edges. I saw Bobby Flay on a show and he said he puts them in boiling water and cooks them for 12 minutes, water shock them for 5 minutes, and peel them. I cook 6-12 at a time so that I have them on hand to use as a snack, add to salads, make egg salad sandwiches, add to tuna for sandwiches. I cook soft boiled for 3 minutes or so, haven't done it often, tho' I really enjoy a couple of soft boiled eggs now and then.
I will have to post a new (to me) Italian Deviled Eggs soon I had them once and then made them the next week!