kahal and kehila

What is the difference between the similar words kahal קהל and kehila קהילה? Both can be defined as "assembly", "congregation" or "community" - but do they have different connotations?

Well, one difference is the frequency they are found in the Tanach. Kehila only appears twice (Devarim 33:4, Nechemia 5:7), whereas kahal appears 122 times. Both derive from the root קהל meaning "to assemble, gather", a verb that also appears frequently in biblical Hebrew. That root in turn derives from the word kol קול - "voice", and according to Klein originally meant "to call together" or "call to to an assembly". (The English word call does not appear to be related.) The two roots are occasionally interchangeable. In Yirmiyahu 51:55, we find the phrase kol gadol קול גדול meaning "large assembly", and there are those that explain the word kehila in Nechemiah as meaning "voice".

A similar case of a connection between "noise" and "group" is found in the word hamon המון. It originally meant "crowd" (and later took on the meaning "abundance"), and derives from the root המה, meaning "growl, roar".

One might think that the word makhela מקהלה  - "choir" is connected to kol, voice, but in its singular appearance in the Tanach (Tehilim 68:27) it also meant originally "assembly".

Let's go back to kahal and kehila. Rosenthal here (discussing the modern usage) says that kehila is a group of people with a common interest or goal ("community"), whereas kahal is only a group of people assembled together, and in modern Hebrew is usually limited to the sense of "audience", or the public in general, such as in the phrase daat hakahal דעת הקהל - "public opinion".

A much newer word is kehiliya קהיליה. Introduced by Ben Yehuda, who intended for it to be the Hebrew word for "republic", it has become a synonym for kehila. It is most commonly used when discussing a community of nations - so a good translation would be commonwealth or federation.