What is the difference between a stew, a braise and a casserole?
How much liquid is used, how the food is cut, and — for one of them — whether the word refers to the dish or the pot.
Braise. Food is partially submerged in liquid, typically coming a third to halfway up, and cooked slowly with a lid on. Usually applied to large pieces — a whole shoulder, a shin, half a cabbage.
Because the food is not fully covered, the exposed top cooks in steam and trapped moisture rather than liquid, and can be browned at the end by removing the lid. The liquid becomes concentrated and is frequently the basis of the sauce.
Stew. Food is fully submerged and cut into smaller, uniform pieces. More liquid, and the result is closer to a thick soup. The liquid is served as part of the dish rather than reduced into a separate sauce.
Casserole. In British usage, essentially interchangeable with stew, particularly when cooked in the oven. In American usage it usually means something quite different — a baked dish of combined ingredients, frequently with a topping and not much liquid at all. It is also the name of the pot, which is where the ambiguity originates.
Why these methods work, chemically. They are for tough cuts with a lot of connective tissue. That tissue is largely collagen, which is unpleasantly chewy — but held at temperature in the presence of moisture for long enough, it converts to gelatine, which is soft and gives sauces their body and mouthfeel.
The conversion needs time more than heat. It proceeds well below boiling, and boiling is actively harmful: high temperature makes the muscle fibres contract and squeeze out moisture, so meat becomes simultaneously dry and stringy while sitting in liquid. The ideal is a bare simmer, which is why the oven — providing gentle, even, all-round heat — is easier to control than a hob.
Why expensive cuts fail here. Lean cuts have little collagen to convert, so long cooking only dries them out.
Why they improve overnight. Flavours diffuse and redistribute, fat solidifies and can be removed, and gelatine sets and re-melts with better texture.