"All" could be used to talk about people, animals, objects, time, etc and is much more flexible in daily use as it could be a pronoun, adjective, adverb, noun... "Everything" is a pronoun and can only be used to talk about the entire group of something, all of the things.
A few examples:
(each and every one of) - All the people here are men.
(nothing but/only) - The shorts are all cotton.
(the only thing) - All I want for Christmas is...
(everything that one is capable of) He gave it his all.
(all of the things) - Everything is going wrong.
However, they can also be interchanged in many cases:
Everything here is broken.
All the things are broken.