Calcination, in general, is to heat the materials up to a certain temperature (marginal below melting temperature) such that very tiny crystals of pure phase (embryos of pure phase) are formed. This process should be carried out on powder since due to high surface area (high surface energy) the reactivity would be very high and hence more homogeneity. Once the phase is formed during calcination then we can compact the calcined powder and heat it at high temperature, just below melting point, which is called sintering. During the sintering process, crystal growth or grain growth in poly-crystalline materials takes place thus a highly dense materials can be obtained.
However, the annealing process is quite different and for different purpose. since, after sintering there might be some residual stress or strain present in the sample, though the amount varies from material to material. To remove the strain, annealing is done. Moreover, the annealing is not limited to this purpose alone rather it has a broad spectrum of application ranging from piezoelectic dipole relaxation, magnetic dipole relaxation, inhomogeneity removal in glass and so on.