Cookware and bakeware
Cooking utensils are the containers in which food is cooked, as well as various implements that manipulate the food. Basic types of pots, pans, casseroles, etc., have characteristic shapes, sometimes with subtle variations, but also can have quite different properties due to their materials.
Principally stovetop
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.
Materials
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.
Cast iron
Cast iron utensils come in plain metal, and in various types of factory coatings. These utensils share the property of having good heat retention and spreading heat evenly.
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.
Mild steel
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.
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.