What is the difference between field theory and particle theory?

1 hour ago, Brainee said:

What is the difference between field theory and particle theory?

In what context?

There is none.
Quantum field theory by necessity, requires quantum particles, as both 'carriers' and 'manifestation' of the field.

If you are inquiring about classical felds, what particles  did you wish to consider ?

“requires quantum particles, as both 'carriers' and 'manifestation' of the field.”

Perhaps, the point where the shells (parameters) of various fields intersect or contact one another –  the a compound moment of two or more fields – that is a manifest particle.