I noticed in Divrei HaYamim II 23:3 (see 23:1-2) the term kahal is being used for a respresentative group ( possibly consists a small number of people who represent a larger group), why is that? P.s. Moshe for example had to speak or to command something to the edah/adat does that mean it only applied to them or did they had to share their knowledge with the people or the kahal? I’m trying to figure out how this worked? For I always thought kahal and adat were synonyms of some kind (like Yisrael and Ya’akov) different names for the same thing.

In Divrei HaYamim there, the Malbim doesn't explain why, but based upon his commentary in other places, the term kahal may come to infer that they were assembled there in a disorganized fashion. Yes, usually when Moshe speaks only to the selected assembled, they then go and pass it on to the others. As opposed to the Malbim, there are other commentaries (e.g. Ibn Ezra, Radak) who often say that similar words are really synonymous, but since you asked about the variance between the terms, I accordingly answered based upon the Malbim who posits that no two words in Hebrew, the Godly language, can be exactly identical, and he almost always explains the difference.