DERIDE, MADE, MAID, MAIL, MISDID, RIDE, WADE, WAIL

The following words have a different something in common:

ACCEPT, ACES, BABOON, PUSHUP, SICK, WOOF, WOOFER

The following list incorporates both ideas, but is also in a particular order:

HE, AM, ACID, ACES, AMAZES, OUTRIDE, ACTIVATE

Of the following, what word best fits as the next in sequence?:

CORRECT, CORRECTION, CORRECTLY, CORRECTNESS, CORRECTOR, CORRECTORS, or CORRECTS

You and Joe both have given the solution, so I've made the official solution public.

I see you've included a 0th Fibonacci. But there are a couple of things wrong with using AR for it.  First of all it's not a word. Second, all the words are presented in all-caps, with understanding that in the case of elements, the second letter of a two-letter symbol needs to be lowercased after the fact.  So AR is also, ambiguously, Ar for Argon. ME would be better, as being a word and representing a state. (ID would also work.)

Also, you correctly use the states and elements in the examples, though that is he opposite of your original statement "States [1] and Elements [0]".