You can do some particle physics without quantum physics, and a lot of quantum physics is applied to other things than what is usually called particle physics (like solid state physics, lasers, nuclear physics, quantum chemistry ...).
In fact, particle physics is now rather called "high energy physics" because it studies essentially phenomena at very high particle energies (in the GeV - TeV range).
Quantum theory is a certain conceptual framework in which certain phenomena can be well described, and in fact there is such a framework for high-energy physics which is quantum field theory.
Your question is a bit similar to: what is the difference between Newtonian mechanics and studying airplane engineering. Newtonian mechanics is a conceptual framework that can be used in the studying of airplane designs, but there are aspects of airplane design that don't need much mechanics, and you can do a lot of other things with mechanics outside of airplane design.
