They used to mean the same thing, in english as little as a century ago. But the meaning of terrible has changed in the last hundred years, to emphasize the meaning 'very bad' instead of 'terrifying' which means something strikes you with fear. Hmm, I notice that the same thing happened to the word 'awful'. It used to mean something would fill you with awe, but now it just means very bad. Why does this happen? I think because people are inspired by their experiences to come up with more different and expressive ways to say how bad things are.

That roller coaster ride was terrifying. So terrible I will never do it again.

I agree with Zooey, Terrible is used to describe a bad experience or situation. (e.g terrible weather or terrible concert) Terrifying is used to describe an experience where you had extreme shock or fear (e.g. terrifying ride in a racing car) Feel free to ask me any other questions :)