All these processes sound like structural change caused by heating.
Annealing is a heat-treatment process for stress-relief of a material. Annealing facilitates reduction of internal stresses and total elastic energy stored in inter-atomic bonds within a treated material. The term is used for appropriate heat-treatments of metals, ceramic glasses, and high-performance polymers. An example would be a cold-rolled steel billet annealed so that it can be worked further into final products. The process of annealing is used whenever internal stress are unacceptable, such as prior to a machining step. Machining changes the distribution of internal stress by removal of material, which is rebalanced by the machined part deforming.
Curing is a heat-treatment process for accelerating a chemical reaction, and is generally used in the context of polymeric and polymeric composite materials. Thermoset polymers which do not set in a reasonable time at room temperature are cured at higher temperatures in a curing oven. An example would be a pre-impregnated or prepreg carbon-fiber mat draped over a mold and then cured so that it retains the shape of the mold. The monomers react much more rapidly at the curing temperature, and form a thermoset polymer, hardening the material prepreg mat. Personally, I have never heard curing applied to any other class of material.
Sintering is a heat-treatment process for causing a powdered material to become a monolithic bulk material by diffusion between individual powder particles. Sintering may occur in either or both of the solid and liquid states. Consider a slurry mixture of alumina powder and wax binder pressed into shape. If the binder is melted off, the alumina powder that remains is only mechanically bonded. That green form may then be sintered to bind the alumina particles together into a monolithic bulk in the same shape as the green form. The same process may conceivably be applied to any material that can undergo diffusion at reasonable rates and temperatures, though it is most commonly used in the context of ceramic and metallic materials, especially high-melting-point refractory metals. Personally, I have never heard it applied to polymers, as their melting points (if such exists) are so low they are simply processed in the liquid state. The process of sintering is used where (1) the material's melting temperature is unreasonably high or (2) parts of acceptable quality may be produced more rapidly by sintering than by casting or machining, such as in low-stress, complex-shaped steel gears.
Knowing the context here might be useful. These terms have nothing to do with each other.
Annealing is warming a metal, usually steel, to give it a soft, easy shaped type of crystalline structure.
Curing is the process of letting a metal sit to work out internal stresses that may have formed during a heat treatment.
Sintering is reducing a metal to a powder and then pressing it together under heat and pressure to form a solid mass. Certain metals, like tungsten, have such a high melting point that it is easier to sinter them into shape rather than cast them. Note that sintering actually technically refers to the process of creating the metal particles, not the pressing.