The Definition of an interacting particle is a particle that CAN interact with other particles. An interacting particle is able to interact with other particles or even with itself (self-interactions are predicted by Quantum field theory).
Quantum mechanics/ Quantum field theory introduces randomness in the Dynamics of particles; this Quantum-mechanical random behavior of a particle gets less random if there are other particles, where the particle does interact with. It is often called "decoherence" or "collapse of wavefunction".
Formally, we can express the loss of random behavior of the particle due to interaction with its surroundings as follows:
Suppose the particle is in state $|\psi> = \sum_nc_n|n>$ where $n$ is a Quantum number like (angular) momentum (orthonormal basis) and $c_n$ the Expansion coefficients at the beginning. The surrounding system is in state $|\phi>$ at this time. Now let the particle evolve in time. It may interact e.g. by self-interactions, vacuum fluctuations. Now we wait until the first interaction with the System took place. At this time, the System changes to $|\phi'(m)>$ induced by the transferring of the Quantum number $m$ of the particle to the system. Moreover, the particle changes to the state $|\psi'(m)>$. Thus, we have the process
$|\psi> \otimes | \phi> \rightarrow |\psi'(m)> \otimes | \phi'(m)>$.
Now, let again be all possible outcomes a Superposition of above outcomes, i.e.
$|outcome> = \sum_m d_m |\psi'(m)> \otimes | \phi'(m)>$
with probability coefficients $d_m$. If we ask for the probability that the outcome will be the transferring of Quantum number $l$, we compute
$|<\psi'(l)|outcome>|^2 = |\sum_m d_m <\psi'(l)|\psi'(m)> \otimes | \phi'(m)>|^2 =$
where orthonormality was used in the second and third line. This is simply a classical probability without any overlap contributions.
Quantum-mechanically, wave functions can also overlap, and due to interaction with surroundings, this overlap is lost; a decoherence took place.