None of them, actually! That is what we can call a myth in the lucid dream community!

We have a very good thread where it's well explained: Sleep Paralysis Demystified

DILD is when you get lucid while already in a dream, and WILD is when you fall asleep while staying conscious, so WILD is the one that is usually, but mistakenly connected to SP. I do recommend you check that thread, though, it's great!