What is the difference between an adjunct and disjunct? How can I distinguish between the two? Please, I will be very thankful if you give me some examples.
As is, your question has no answer, since you haven't mentioned what theory or whose classification you were interested in. Here's what Hilde Hasselgård writes on this:
"A striking feature of descriptions of adverbials is that there are hardly any two grammars that use the same classification scheme and/or terminology" (Hasselgård 2010: 21).