All three cook food gently for a long time, and they are not the same technique. What separates them is the medium the food sits in and how precisely the temperature is held.
Sous vide
Food is sealed in a bag and cooked in water held at the temperature you want the food to reach. Because the water is never hotter than the target, the food cannot overshoot it — which is what the method is for. Time controls texture rather than doneness.
Confit
Food is cooked slowly submerged in fat. Traditionally it is also a preservation method: the cooked meat is stored under the fat that cooked it, sealed from air. The fat is a medium for even heat, not a frying medium — the temperature is far below frying range.
Slow cooking and braising
Braising cooks food partly submerged in liquid, in a covered pot, so that the exposed part is cooked by steam. A slow cooker is an appliance for holding that at a low temperature unattended. Both rely on time and moisture to soften connective tissue.
The practical consequence: a temperature from one method does not transfer to another. A sous vide recipe's 55 °C describes the finished food; a braise's low oven describes the pot.
