Thanks for giving eggs back to us again ;-)
perhaps, the difference between 'omelette' and 'scrambled egg' is when we beat the eggs. We beat up the eggs before we put in a pan to make omelette, but we beat up the eggs in the pan during the cooking to make scrambled ( s - แคร้ม - เบิ่ล ลืด) eggs. [Of course, oil is optional is these recipes.]