Cookware and bakeware
Cookware and bakeware are vessels or containers used to cook food. Cookware refers to items which are principally used on a stovetop, while bakeware refers to items that are principally used in an oven. The distinction is not rigorous; ovenware may be used to sear food prior to transfer to an oven for braising, while cookware may be placed under a broiler to brown the food surface.
These comprise the "pots and pans" category, which are usually used on a gas or electric heating element. Some are made of materials safe to put in an oven for slow heating, or under a broiler for browning.
While most of the cooking variation comes from the primary material of the part of the utensil that contacts the food and the heating utensil, handles, covers, and other accessories need to be considered. A given pan, for example, might not be able to go under a broiler because its handle cannot resist the heat there.
Some cookware is made of multiple materials that transfer heat. For example, stainless steel is a poor conductor of heat, but has the advantage of not reacting with foods and being easy to clean. Many high-grade stainless steel pots, therefore, are made of a sandwich of stainless steel covering aluminium.
Copper is the best practical conductor of heat, but it does react with some foods, even producing toxic chemicals in some cases. Most copper cooking utensils are lined with a thin coating of relatively inert tin.
Cast iron utensils come in plain metal, or with various types of factory coatings. These utensils share the property of having good heat retention and spreading heat evenly. Cast iron utensils are generally the heaviest for a given shape, but need to be handled with care, because they will crack or break if dropped on a hard surface.
Uncoated cast iron, without treatment, will rust if allowed to dry while wet. Some cast iron utensils, such as griddles, never contain large amounts of fluid, and can be wiped dry and safely put into storage, perhaps with light oiling.
More commonly, uncoated cast iron is seasoned, or treated with oil and heat until a thin, stick-resistant film forms on the surface. Even though a new uncoated pan may be a metallic gray when first purchased, a properly seasoned surface will become black.
There are a number of ceramic coatings for cast iron, some of which are extremely durable and extremely expensive, but the more reputable manufacturers offer lifetime guarantees.
Lightweight steel, almost always coated with a ceramic, is popular for such things as large vessels for boiling and steaming seafood, or preparing stocks and sauces. This is also common in home-grade ovenware. Thin rolled steel, which also must be seasoned if it does not have a factory coating, also transfers heat well and can be very useful for quick sauteing.
While the color can vary, the most common ceramic in the U.S. is a dark blue dappled with white spots. If the ceramic cracks from the surface, the steel underneath will rust, but there are repair coatings that can be brushed onto small areas. This type of cookware is relatively inexpensive, so a seriously rusted piece is reasonable to replace.
Stainless steel is especially good for cooking acid foods that might react with metal, corroding the pan, taking on a metallic taste, or both. It is easy to clean.
The major problem with stainless steel is that it is a relatively poor conductor of heat, and, where it does conduct heat, it may do so unevenly. One way to even the heat is to put it on a flat heating element, or to put a heat diffuser under the pan. Another method, which makes the cookware more expensive, is to make it from multiple layers of metal.
Layered stainless steel is not a simple matter of sandwiching a sheet of aluminium between a stainless steel liner and casing. First, the heat transfer properties are such that multiple thin sheets, typically 5mm, work better than a thick one. Second, the arrangement of the heat-conducting material will vary with the purpose and design of the container: how it needs to conduct heat. One high-end manufacturer, Demeyere Apollo, uses a thick bottom of seven plies for pans that only need to conduct heat to the inside bottom. When heat is needed on the sides, as with a stockpot, the aluminium sandwich extends up the sides.
Stock and sauce
A stockpot is straight-sided, and, by European convention, has an equal height and diameter, although some American stockpots are taller than they are wide. It is most often anodized aluminium or stainless steel. They also may be in ceramic-coated steel. Cast iron would be far too heavy to use for a large stockpot. Some are very large, and may have a spigot at the bottom so liquid can be drained without lifting a heavy vessel. Indeed, many commercial kitchens have water faucets over the stove, for filling large stockpots; some commercial and home chefs place the stockpot on the stove after putting in the ingredients other than water, and then fill it with a hose. They usually have two handles.
Saucepots are still deep vessels, but relatively wider and shorter than a stockpot of equivalent size. The European convention is that their height is two-thirds of their diameter. Increased surface area, compared to a stockpot, helps reduce the volume of liquid, as might be desired for a soup. They most often have two loop handles.
While generally keeping the proportions of saucepots, straight-sided saucepans have a single long handle, which, even if metal, may not conduct heat well so it can be grasped without hand protection. Large saucepans may have a supplementary loop handle on the side opposite the long handle. In European practice, a saucepan typically half as high as its diameter.
Saucier pans, however, vary the shape but not the proportions of saucepans; rather than straight sides and a flat bottom, they have flared edges and a rounded bottom to facilitate stirring and whisking. These would be used for sauces and other preparation that need more agitation than gentle evaporation; a saucepot is preferred for the latter application. Yet another variation, with many names: Windsor Pan, Splayed Saucepan, Fait Tout Pan, Evasé Pan, keeps the flared sides but flattens the bottom. The Windsor pan lends itself to stirring but not whisking, but is superior to a saucier pan when the sauce is to be reduced (i.e., evaporated) and stirred. 
Double-boiler inserts are available for many saucepans. These are used to apply a very gentle heat, with the only heat reaching the insert containing the food being applied by steam coming from water in the bottom.
While the double-boiler insert holds liquids such as sauces or thick preparations such as polenta, a similar perforated insert can be used to steam small amounts of food.
Asparagus steamers are even narrower, for their height, than a stockpot. They are equipped with a lift-out basket, often of fairly widely spaced wire. These can be used for other boiled foods, such as corn on the cob.
Pasta cookers, especially those intended for long pasta such as spaghetti, may be much like an asparagus steamer, only with a tighter mesh or perforated metal basket. Pasta cookers optimized for small pieces of pasta tend to be wider. Another term for the type is the pasta pentola.
Large steamers, often used in Asian cooking, are made from a set of perforated pans that nest, one on top of another, over a bottom containing boiling water.
Foods cooked in flat pans are not submerged in liquid, or, as in poaching, in a very small amount, far less than in a deep pot. These utensils vary with the height and shape of the sides of the pan; griddles allow use of the widest spatulas.
Omelet pans have very low sides, so that an omelet easily can slide over them. Some cooks use pairs of identical omelet pans, cooking one side and then dropping the half-cooked omelet into the mating pan, to cook both sides without the need to "flip" the omelet. Other cooks, of course, are proud of their ability to flip omelets either with spatulas or with an experienced wrist motion.
Somewhat higher sides, the European standard being 1/3 the diameter, are on the sautoir' or sauté pan, which has a single long handle, on large pans, a second loop handle. The name derives from the French word sauter means "to jump." In the saute process, the cook moves the pan, tossing the food, rather than manipulating it with a spatula or spoon. U.S. All-Clad's sauté pans are shallower than the typical European sauté. Unless the cook has immensely strong wrists, saute pans must be made of lightweight material such as aluminium or steel.
A braising pan, also called a braiser, rondeau, or buffet casserole has the same proportions as a saute pan, but two loop handles. Rather than sauteing, the pan is used to sear foods, typically moving it with a spatula or tongs, then adding liquid, covering the pan, and finishing the oven. Standard braising pans are straight-sided, but there are also various slope-sided types, shallower than a braiser and with a domed lid. The sloped side makes it easier to turn items with a spoon or spatula, rather than simply moving them on the cooking surface.