How does food cook differently on an open top grill than a covered one

I believe the goal is to get the best sear possible on each side of the meat. Moving the meat around too much could cause it to cook completely without getting a good sear on the outside.

Clearly this doesn't apply when doing anything "rotisserie" style, as you're trying to do the exact opposite: slowly cook the interior of the meat without burning the outside to a crisp or unevenly.

Also, see this similar question: Grilling burgers: flip once, or keep flipping?

Simple answer: fewer briquettes. Space them out a bit. You can make fine adjustments by raising the cooking surface or lowering the briquettes. I know my kettle has a lower briquette grill, if you take out the main one. I've also seen briquette grills with sunken channels to create small pockets of heat. I also have a couple of trapezoidal briquette holders, which I can use to position briquettes and create warmer or cooler spots.

Charcoal briquettes are designed to be a consistent temperature. Of course, poorer quality briquettes will be less consistent or burn for less time, but in general any single briquette will burn as long and as hot as any other.

Trying to douse or smother the briquettes may cause smoke or steam, but it's not going to have a good, consistent effect.

Interesting comparison info from Dutch Oven cooking: with a standard 12" Dutch Oven, 12 briquettes in a ring under the oven and 12 spaced around the edge of the lid will give you approximately a 350 degree oven for about an hour. Temperature is adjusted by adding or removing briquettes. This means, in a grill, 24 briquettes could give you a grill temp near 350, if the food is about 2-3 inches away. (The linked chart has a slightly different arrangement; 12/12 is what I learned as a simple rule of thumb, but everyone has different practices... or may desire top browning or bottom boiling.)