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Sauteeing is finished when your item is cooked in the frying process. Braising takes further in that once you get the meat all browned, you add water, or stock, bring to a boil, reduce the heat to simmer and cover it, cooking it slowly until it's fully done and tender.

Sauteeing is also more suitable for thin or small or very tender cuts or meats and fish, where braising is used to get tenderness out of tough cuts and large pieces.

I assume you're talking about beef. There's not a great deal of difference (by definition) between stewing and braising; although I think "stewing" implies a longer cooking time. The reason they refer to the beef as "stewing" or "braising" meat is because it comes from a tougher cut, such as the shoulder. If you simply grilled meat such as this, it would taste just fine, but it would be very hard to chew. There's also more connective tissue and sinew. When you braise (or stew), you're cooking the meat in some liquid, for a rather long period of time (ideally, the liquid shouldn't be rapidly boiling during the cooking; it should be just barely simmering). So, whichever kind of meat is available, it'll work just fine.

Sauteeing is a Dry Cooking Method

frying: cooking in fat or oil in a pan or griddle

Braising is a Moist Cooking Method and Dry Cooking Method

by browning in fat, then simmering in a small quantity of liquid in a covered container.

Hope this helps

Ruby,

Braised foods are sauteed, then cooked in a covered casserole with a small amount of liquid.

Sautéeing

sauteing is browning the ingridients only on the outside(usually done in high heat) i think brasing can only be done with meat and its when you braise the meat until caramelized on the outside(usually done in medium heat) if i had to chose between the two i would chose brasing. but ofcoures sauteing is perfect for begetables.