Explaining why FFT is faster than DFT for the general public?
FFT is an algorithm for computing the DFT. It is faster than the more obvious way of computing the DFT according to the formula.

Trying to explain DFT to the general public is already a stretch. Also, they probably don't know what an algorithm is. Perhaps you could say that there's a fast way of computing the DFT, and that's one more reason why it's so useful.