I add salt and pepper and a little milk (about 1 tbsp per egg) to the eggs, scramble them up, making sure that the whites are completely mixed, toss in a pan with a little butter. I don't like them runny but I also don't like them cooked hard. I like them where they just hold together, if that makes any sense
I call scrambled eggs that have stuff added to them "breakfast scrambles". To me, an omelet is solid with the fixin's folded in the middle. If the fixin's are mixed in with the eggs and it is cooked as one solid mass, I call it a frittata.