Both Kanthal and Nichrome are high temperature wires.
Kanthal is the trademark (owned by Sandvik) for a range of iron-chromium-aluminium (FeCrAl) alloys used in resistance and high-temperature applications. The first Kanthal alloy was developed by Hans von Kantzow in Sweden.
“Kanthal alloys consist of mainly iron, chromium (20–30%) and aluminium (4–7.5 %). The alloys are known for their ability to withstand high temperatures and having intermediate electric resistance.” So, it is often used in kiln elements.
“Kanthal forms a protective layer of aluminium oxide (alumina) when fired.” This layer resists further oxidisation of the elements when firing. Aluminium oxide is an electrical insulator with a relatively high thermal conductivity. Ordinary Kanthal has a melting point of 1,500°C.
“Kanthal is used in heating elements due to its flexibility, durability and tensile strength.” Its uses are widespread, with it being used in home appliances and industrial applications as well as glass and ceramic kilns. As an aside, it is being used in electronic cigarettes as a heating coil as it can withstand the temperatures needed in this application.
Based on Wikipedia https://en.wikipedia.org/wiki/Kanthal_(alloy) and other sources.
Nichrome is an alloy of various amount of nickel, chromium, and often iron. The most common usage is as resistance wire. It was patented in 1905.
“A common Nichrome alloy is 80% nickel and 20% chromium, by mass, but there are many other combinations of metals for various applications.” Nichrome is silvery-grey, corrosion-resistant, and has a high melting point of about 1,400°C.
It has a low manufacturing cost, it is strong, has good ductility, resists oxidation and is stable at high temperatures. Typically, nichrome is wound in coils to a certain electrical resistance, and when current is passed through it, the resistance produces heat. This is probably the most common material used for kiln elements.
When heated to red hot temperatures, the nichrome wire develops an outer layer of chromium oxide, which is stable in air, being mostly impervious to oxygen. This protects the heating element from further oxidation. However, once heated the nichrome wire becomes brittle and must be heated to red hot before bending.
Based on Wikipedia https://en.wikipedia.org/wiki/Nichrome and other sources.