"Geometric" - Geometric collision criterion
The geometric collision criterion calculates the two-particle impact parameter as the closest approach distance in the two-particle center-of-momentum frame by boosting to the respective frame. The collision time used for the ordering is calculated as the time of the closest approach in the computational frame.
For further details, see Bass:1998ca [1].

"Stochastic" - Stochastic collision criterion
The stochastic collision criterion employs a probability to decide whether particles collide inside a given space-time cell. The probability is derived directly from the scattering rate given by the Boltzmann equation. The stochastic criterion is the only criterion that allows to treat multi-particle reactions.
For more details, see e.g. Lang et al. (1993) [4].

Note: The stochastic criterion is only applicable within limits. For example, it might not lead to reasonable results for very dilute systems like pp collisions. Futhermore, the fixed time step mode is required. The assumption for the criterion is that only one reaction per particle per timestep occurs. Therefore, small enough timesteps (Delta_Time) have to be used. In doubt, test if the results change with smaller timesteps. Since the probability value is not by defintion limited to 1 in case of large timesteps, an error is thrown if it gets larger than 1.

"Covariant" - Covariant collision criterion
The covariant collision criterion uses a covariant expression of the two-particle impact parameter in the two-particle center-of-momentum frame, which allows for its calculation in the computational frame without boosting. Furthermore, it calculates the collision times used for the collision ordering in the two-particle center-of-momentum frame.
Further details are described in Hirano:2012yy [3].