I am going through a literature where these terms are regularly used and I am confused are they different and if yes then what does each term mean? I also want to know relation of plastic strength of a rock (say granite) with pressure. I mean which equation describes this relation?
All these terms refer to the effect of loading on the deformation of materials. Let us assume that we start with zero load and zero deformation.
If you increase the load you get an increase in deformation. During the process of elastic deformation, if you decrease the load to zero you will not have any residual non-zero deformation.
The process during which the material deforms to such an extent that when the load is removed the deformation does not return to its initial state. The material appears to flow like a fluid.
Plastic yield strength
The load beyond which elastic deformations cease to occur.
This term is not specific enough and typically not used when technical accuracy is desired.
This is another term that does not mean much and should be avoided. An alternative is the yield stress which means the same thing as plastic yield strength
Relation between yield stress and pressure
The term pressure can have multiple meanings depending on the context.
If you are thinking of a load applied to the surface of a rock sample, there is no straightforward way of relating the yield stress to the applied load. There are numerous models for rocks and other granular material. See https://en.wikipedia.org/wiki/Yield_surface.
On the other hand if you are thinking of the change in hydrostatic yield stress with plastic strain, crush curves are typically used to model the evolution of caps on yield surfaces. See http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/15/061/15061729.pdf#page=43 for an example.
Rate-dependent plasticity If you load a rock sample in uniaxial strain compression at various speeds, the load at which it yields will appear to increase with the speed of loading. If you define the yield stress based on a low speed (quasistatic) test, the stress will appear to exceed the quasistatic yield stress.