For example, when making a turkey for Thanksgiving, I generally place it in the oven (covered in foil or a turkey bag), and cook it for many hours at the recommended heat setting.
I can crock-pot a "roast" cut of meat for many hours, or put it in the oven (again covered) for several hours at a low temperature.
How is that different from "baking", other than when baking the top is generally not covered?
Traditionally roasting used radiant heat to cook meat. This would have taken place over an open flame, typically on a rotating spit. In modern times this method is now called Rotisserie. Modern roasting refers to dry heat cooking that takes place in an oven, the food is cooked by convection. Until the late 19th century this method was referred to as baking.
Baking is essentially the same as roasting in modern times. Baking most often refers specifically to the cooking of "baked goods" (breads, pastries, etc.). However, the terms baking and roasting are often used interchangeably (baked chicken, roast chicken). There doesn't seem to be a hard and fast rule here as to which term is used. For example, you roast asparagus, turkey, chicken, but bake lasagna, casseroles, and also chicken.
Braising uses a combination of moist and dry heat to cook the food. This is what occurs in a crock pot, or in dutch oven/stock pot in the oven. Your meat will be cooked in an ample amount of seasoned liquid such as wine and/or stock.
Broasting I had never heard of before. According to Wikipedia it's a trademarked method of pressurized deep frying. I doubt this is what you were referring to.
According to ochef these days baking and roasting are the have become synonyms, although they were not always so. Broasting, as you can see from the definition, is not a dry heat application and is therefore different.
For everyone who says roasting involves meat and baking is everything else, you can point to all the roast vegetable recipes (although I have yet to hear about a roast cake, pie, or cookie recipe). For everyone who says roasting is a higher temperature than baking, you can point to slow roast recipes that cook for a long time at a low temperature. The best way to determine the difference is convention - if an item is normally roasted, call it roasting. If it's normally baked, call it baking.
for me, roasting implies adding oil in some way, even if this only comes from the oil present in the cut of meat, and not emulsified oil, like the butter in a cake.
baking implies dry heat and no 'loose' oil.
roasted veg would have oil on them, baked potatoes do not. A pie or chicken kiev would be baked as no oil is added, a whole chicken would be roast as it would release fats as it was heated, even if no additional oil or butter was rubbed in.
Update - after talking it over with a friend the actual temperature might come into it. Things seems to be baked at a lower temp say up to 180C and roast above say 200C, but its not a hard and fast rule.
Broasting is generally used for deep frying using oil in the pressure cooker instead of water. The word is probably a portmanteau of "boiling" and "roasting".
While it used to be a common trick with vintage pressure cooker manuals, all modern home devices warn against the practice. Please do not attempt at home unless you have the restaurant grade equipment that says it is specifically for broasting.
KFC cooks their original recipe chicken (not their spicy crispy recipe) this way. They use an industrial cooker and heat the oil up very hot to start, and then they add a weighed batch of chicken and seal the lid. The hot oil rapidly crisps the outer coating while the chilled chicken drops the temperature of the oil downward as it cooks.
Simply roasting is shallow frying and broasting is deep frying
