Subsidence is nothing but sinking of large (considerable) area of ground surface in downward direction. Subsidence may be a consequence of extraction of groundwater and soil as well.
These extractions may lead to compression of underlying soil (porous texture) or sometimes rock structure. The subsidence is considered as secondary influence on foundation settlement as no direction influences are observed (as of consequence of extraction of groundwater or oil).
So the settlement of structure above it due to this is considered secondary settlement. Other than extraction, there have special case of downward displacement where wet clay deposit remain in soil strata.
Foundation suffers downward displacement when wet clay deposits are dried out and very often downward displacement of foundation due to desiccation of such layer are termed as settlement.
These displacements are not always downward; the reverse displacement is also observed. In rainy season when moisture is introduced to clay deposit the expansion of volume of deposit is happened in some active clay soil. We have discussed about activity of clay in our previous post.
In such case, initially settled foundation may be even heaved. So it is not a permanent settlement (in case expansive clay). The seasonal influence in such deposit may lead to cyclic shrinkage and heave on foundation soil and should be carefully studied. We have published many posts about expansive soil in our previous posts.