The difference is in the way they're used. Кто-нибудь is used in questions, всякий is (usually) used in statements. For example:Originally Posted by Darobat
A guy at a meeting holds up a diagram, looking confused, and asks: Кто-нибудь это понимает?
Somebody from the back answers: Да всякий должен это понимать!
Hmm...thinking about it over again, there's probably a little difference in meaning there, more than I saw before. Here's a better (I hope) translation:Originally Posted by Darobat
не всякий может это понять = not just anyone can understand that, meaning that the average person probably won't get it, whatever it is. So все and всякий aren't really interchangable without changing the meaning of the sentence.
Sorry about the confusion!