These two words are not usually interchangeable. They do not mean the same thing. If people keep using them improperly, Banger will be forced to take drastic action to make a dramatic statement about the use of these two words.
Drastic means severe or serious. It implies something negative–that is its connotation, or the feel of the word.
In a sentence, you might say: “His sprained ankle caused a drastic reduction in his ability to run.”
Drastic implies something bad.
Dramatic means sudden or extreme. Things that are dramatic do not need to be negative–the word does not have that connotation.
Thus, in a sentence, dramatic might be used as, “Her new haircut was a dramatic change which suited her.”
In this sentence, dramatic implies big.
Sometimes things can be both drastic and dramatic:
“The 50-degree drop in temperature was both dramatic and drastic.” The change was both sudden and severe, so it was drastic and dramatic.
Still unsure of which to use? If you can substitute the word bad where you’d use either drastic or dramatic, you should use drastic. If you can substitute the word big, use dramatic.
Hope that helps. If you still have questions, leave a comment below!