Not sure exactly how sub-cooled ice differs from regular ice. But, I have seen the inside of a restaurant ice machine, and the way it makes ice is different from the standard, put water in tray, put tray in freezer, wait for solid cube.
A restaurant ice machine produces ice, by cooling a plate that has ice cube shaped holes in it. The plate is oriented vertically. A pump circulates water to the top of the plate, and then it dribbles down the plate like a waterfall. The bottom of the plate has a tray for the pump to collect and re-circulate the water that did not freeze. Additional water is added to the tray via a float (very similar to a carburetor or your bathroom toilet) as the water level drops due to the ice on the plate.
When a sensor on the front of the cold plate senses that the bridge depth between cubes has been reached, the plate gets warm, and a sheet of ice cubes approx 2 x 3 feet drops straight down to the collection bin, where the bridges between the cubes break on impact. (Due to the angle of the plate the falling cube sheet misses the collection tray when it falls)
The collection bin, although it generally is big enough for two grown men to easily hide in, doesn't contain any additional cooling.
The ice does differ from homemade ice in that it looks clearer. The clarity of the ice I would assume is due to the circulating flow of water freezing in little micro layers rather than as one big mass. Perhaps when frozen as one big mass, the outsides freeze and the air in the water (yes air in water, how did you think fish breathe?) at the center of the cube isn't able to escape and is frozen like Han Solo. Thus a cloudy ice cube.
Well I've been up too late, way too much rambling. (When I use Han Solo, talking about ice it's a sure sign that it's time to go to bed.)
Later! Happy Beverage to you.
Jeffrey MackoThe Royale Cinema