Getting confused

I’ve been preparing some material on sentence composition and managed to confuse myself after trying to understand the difference between adjuncts and adverbials.  Adverbials can be adjuncts apparently, but not always.  Then there is presenting all these nuggets of grammatical knowledge to students in a manner which will actually improve their written (and spoken) English in an effective and, preferably, non-confusing manner.  Fun, fun, fun.
I shall have to test this material thoroughly and monitor its long term benefits.  All I need are a few willing victims, sorry, er, guinea pigs.