Particle production in two-photon interactions at hadronic collisions is becoming increasingly relevant in the LHC physics programme as a way to improve our understanding of the Standard Model and search for signals of New Physics. A key ingredient for the study of these interactions in $pp$ collisions is the description of the photon content of the proton, which allow us to derive predictions for the cross sections associated to events where occur the proton dissociation (non - exclusive processes) and for those where both incident protons remain intact (exclusive processes). In this paper, a detailed comparison of the different models for the elastic and inelastic photon distributions found in the literature is presented and the current theoretical uncertainty is estimated. The impact on the invariant mass distribution for the dimuon production is analyzed. Moreover, the relative contribution of non - exclusive events is estimated and its dependence on the invariant mass of the pair is presented. We demonstrate that the predictions for production of pairs with large invariant mass is strongly dependent on the model assumed to describe the elastic and inelastic photon distributions and that the ratio between non - exclusive and exclusive cross sections present a mild energy dependence. Finally, our results indicate that a future experimental analysis of the non - exclusive events will be useful to constrain the photon content of proton.
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