An alternative way to interpret a model in COPASI is as a stochastic process. In this context, reaction kinetics do not represent the rates of change in species concentrations. Instead, they specify the probability that a reaction event occurs. When a reaction event takes place, the particle numbers of the involved species are updated based on their stoichiometries. As a result, particle numbers are always integers and change in discrete steps.
The value of the kinetic function is interpreted as a propensity, which is a differential probability density indicating the likelihood that a reaction event will happen within the next infinitesimal time interval. However, there are subtle differences between reaction rates and propensities. For example, this difference becomes important for small particle numbers. The rate of a second order mass action reaction is expressed as $k \left(\frac{S}{V}\right)^{2}$, whereas the propensity for the same reaction is $k \, \frac{S}{V} \, \frac{S-1}{V}$. COPASI applies these types of corrections automatically. If you have already manually included such corrections in your model, you must instruct COPASI not to apply them a second time. Instructions for this can be found in the general model settings.
Another important point to consider is that enzymatic reaction rate laws derived from the steady state approximation are not always valid for stochastic simulations. While often applicable, the assumptions made in their derivation do not exactly match those for deterministic simulations.