A pulse–pulse interaction that leads to rogue wave (RW) generation in lasers was previously attributed either to soliton–soliton or soliton–dispersive-wave interaction. The beating between polarization modes in the absence of a saturable absorber causes similar effects. Accounting for these polarization modes in a laser resonator is the purpose of the distributed vector model of laser resonators. Furthermore, high pump power, high amplitude, and short pulse duration are not necessary conditions to observe pulse attraction, repulsion, and collisions and the resonance exchange of energy between among them. The regimes of interest can be tuned just by changing the birefringence in the cavity with the pump power slightly higher than the laser threshold. This allows the observation of a wide range of RW patterns in the same experiment, as well as to classify them. The dynamics of the interaction between pulses leads us to the conclusion that all of these effects occur due to nonlinearity induced by the inverse population in the active fiber as well as an intrinsic nonlinearity in the passive part of the cavity. Most of the mechanisms of pulse–pulse interaction were found to be mutually exclusive. This means that all the observed RW patterns, namely, the “lonely,” “twins,” “three sisters,” and “cross,” are probably different cases of the same process.