I think "terrible, horrible, appalling, atrocious" are synonyms of "awful". But how are they different?
You're right, these are all synonyms of "awful". The main difference is in their formality. "Terrible" and "horrible" are more commonly used because they do not sound very formal and can be used in everyday conversation. "Appalling" and "atrocious", especially "atrocious" sounds much more formal and is not used very often in daily conversations or in any conversation unless it is super formal.