Generally, they mean the same thing. e.g. The car accident was a/an terrible/awful thing to see. I feel awful/terrible. They are interchangeable.

Originally, the word "awful" meant something that filled you with awe or something that caused reverential fear. You could say the destruction you saw after the tornado was "awful". However, today, the word is commonly used to describe something bad or unpleasant. The word "terrible" also means something that causes fear or terror. It is used informally to describe something of poor quality. For example, you might hear people say,"the workmanship of this product is terrible". Generally, the word "awful" would be considered more extreme. People usually say the word "awful" with more emphasis. For example, when you hear about a mass suicide, you might say, "that's awful!!". I hope this helps.

I think that the terms are not fully interchangeable, you can say to a person "you are terrible!" or "you are awful!" and certainly the two expressions had a different meaning, terrible refers oftenly to behavior or performance and awful to apparence or even taste. You may say "the singer are terrible!" or "her little brother is terrible!" And "That soup is awful!" or "that is an awful wound!" Is my humble oppinion.