There are a number of different types of nuclear fuel in terms of what isotope is used, what other materials are mixed with the isotope and the physical configuration of the fuel. Nuclear reactors are designed to use a specific isotope in a specific shape
The metal oxide form of uranium is used in many reactors because it has a higher melting point than pure uranium and it cannot burn. A series of chemical reactions is used to create uranium dioxide which is pressed into pellets and fired to create a dense solid material. This type of fuel is called UOX.
Plutonium is blended with natural uranium or uranium that has already been depleted in fission processes to form a mixed oxide fuel called MOX. MOX is an alternative to the nuclear fuel used in most reactors and is a way to dispose of plutonium by transmutation.
Metal alloys are also used for nuclear fuel. These include pure uranium as well as uranium alloyed with aluminum, zirconium, silicon, molybdenum. These fuels have the highest fissile atom density but cannot survive high temperatures like the oxide fuels.
There is a nuclear fuel called TRIGA which is made of uranium zirconium hydride. As the temperature of the core increases the reactivity of TRIGA decreases which makes meltdowns improbable. This fuel is often used in reactors which produce neutrons for nuclear research.
Uranium nitride is often used in NASA reactors and has the advantage of a very high melting point when compared to UOX. However, the best nitrogen isotope for this fuel is very expensive which reduces the desirability of this nuclear fuel.
Uranium carbide was studied in the 60s and 70s but is not widely used as a nuclear fuel. It has a high thermal conductivity and a high melting point and the absence of oxygen makes this an attractive fuel. It may be the fuel of choice for the fourth generation reactors currently under development.
Some liquid fuels have also been developed for use in reactors. The big advantage of liquid fuels is that they can be easily controlled but the big disadvantage is that they can easily leak out of the reactor if there is an accident. They are mixtures of lithium, beryllium, thorium and uranium fluoride salts used in molten salt reactors.
All of the fuels discussed above are used in nuclear reactors. Radioactive materials can also be used in what are called atomic batteries. Plutonium-238, curium-242, curium-244 and strontium-90 have been used for this purpose. Atomic batteries can be non-thermal and use alpha and beta particles for energy generation or thermal which convert heat directly to electricity. Some thermal generators just use the heat from the decaying radioisotope.
All these different fuels have their advantages and disadvantages based on their cost of production, thermal conductivity, neutron production, ease of handling, combustibility and a variety of other considerations.