What's a "single-camera" show?

So a single-camera show is a filming style, not a narrative style. Got it.

Is there a name for quasi-mockumentary semi-improvisational comedies? Such as Arrested Development and Reno 911?

Haven’t seen Arrested Development, but Reno 911 is a mockumentary (documentary if it was real) and some would also say it’s shot reality tv style or run 'n gun. Again usually shot single camera with a boom mic.

Indeed, Desi Arnaz is often attributed as the inventor of the three-camera system.

Arrested Development isn’t even a semi-mockumentary, in that there’s no awareness at all on the part of the characters that they are participating in making the show. It’s just an uncommonly well-scripted sitcom filmed single-camera style, with little or no improvisation that I am aware of. Curb Your Enthusiasm, however, is heavily improvised IIRC.

I think your question does serve to underscore the fact that single-camera sitcoms are almost becoming a genre unto themselves, with a density of gags and a fast-cutting style that the 3-camera shows can’t match.

The soundstage big enough to accomodate a live audience will have different acoustics than the more intimate studio where a soap opera is videotaped. Otherwise, the sound recording media are the same.