What is the relationship between many particle and fields?

In statistical mechanics, you can take the hydrodynamic limit and get statistical field theory. In quantum field theory, you can show that the system acts like a quantum many particle system. There seems to be this natural correspondence between many particle and field ontologies.

Because the basic assumptions of quantum and statistical theory are so related (roughly, quantum assigns amplitudes and statistical assigns probabilities), I’m wondering if these two correspondences are manifestations of the same underlying structural similarity between many particle and field systems.

If not, I was just wondering if anyone could enlighten their relationship and how these two manifest in the systems.