Question: The people of Israel are sometimes called collective Kahal (קהל), sometimes Edah (עדה ,עדת) and sometimes plain Israel, and although they probably point to the exact same group of people they seem to be well chosen. What’s the nuance between the usage of Kahal and Edah?

Besides refering to Israel, it’s also used for example in Bamidbar 16:6 to describe the group of people of followers of Korach as an Adas (עדת), while another group of people in Ezra 10:1 is called Kahal (קהל). And Bamidbar 20:2 seems to clearly distinguish between these two words.

So when do we refer to a group of people as an Edah or Adas, and when as a Kahal?

Answer: I really love the question! This brings me right back to my first days at Yeshiva Ner Yisroel, where my rebbi, Rabbi Ezra Neuberger, gave one of his “homework assignments” in studying Chumash (not part of the regular Yeshiva curriculum): Pick two Hebrew words that seem to be synonyms – say two words for sheep, Keves and Kesev – find the places they appear in the Torah, and figure out what they really mean and how they differ. I learned a lot when I did it.

You seem to have made a great start on your assignment! I really don’t want to do it for you, you’re doing fine. I did see that Bamidbar Ch. 14 has a lot of interesting references, including 14:5 which mentions both words.

A few good places to look – though I can’t tell you where in this particular case: Rav Shamshon Raphael Hirsch, the Malbim, the Netziv in his Emek Davar. Each of these very frequently tries to figure out the meaning of Hebrew words, or compares similar ones, by looking through the examples where they appear.
Maybe helpful:

Looking at some words with the same structure (shoresh), Kahal seems to mean “gather everyone together”, “form into a big group”. For instance, see D’varim 31:12 for the Mitzvah of “Hakhel”, gathering all of Israel to hear the Torah read.
And “Edah” has the same Shoresh (root) as “Va’ad”, a meeting. See Bamidbar 16:11, “Noadim al Hashem” – gathered (against) Hashem. Shemos 25(22): “V’noadti L’cha Sham” – I will meet with you there.
So I would assume that Kahal is the word that refers to the gathering process, and Edah the word that refers to the result of the gathering, the meeting. If that’s right, you’d have to see how it plays out in the various cases.

But please continue with your very worthy investigation.

All the Best, Michoel Reach