What's the difference between the term "kahal" (from the root: to gather) and the term "eidah" which I can't even guess what's its root!

Often translators unfortunately don’t differentiate between the fine differences of terms. The Malbim explains that the shoresh (root) of “eidah” is mo’ed (like a holiday=mo'ed, has an appointed time and we get together by respective families) or va’ad (=committee), which means a meeting at a particular place, with particular people, for a particular purpose, where the participants congregate according to their role. For example, the judges, elders and leaders, who are the main figures in a public meeting, are separate from the masses, to enable proper discussion or questions (Shmot 35), or when meeting by family (Korban Pesach, Shmot 12) or traveling by tribes (ibid, 17). On the other hand, “kahal” is simply the crude mass gathering together of people, without delineating who in the group is where, like we find by the uprising against Moshe in the sins of the golden-calf (Shmot 32, 1) and the water complaint in Mei Meriva (Bamidbar 20, 2). On the other hand, our rabbis point out that in the first water-uprising (Shmot 16), they are called eida, because they came organized, led by the elders, and not just gathering up altogether to yell. Accordingly, the 1st time, they were not punished nor severely admonished. It’s the difference between “meeting” (eida) and “gathering” (kahal). In Korach’s uprising, they are called eidah (Bamidbar 16), because even though many came together, there was a hierarchy in their uprising (Korach, Datan and Aviram were the clear leaders), and they had meetings (“mo’ed”, not just yelling!) with Moshe. Similarly when both terms are found together (e.g. Vayikra 4, 13), the eidah refers to the Sanhedrin judges who met and made a mistake, and afterwards the masses (kahal) acted upon their ruling.