It has been proposed that S0 galaxies are either fading spirals or the result of galaxy mergers. The relative contribution of each pathway and the environments in which they occur remain unknown. Here, we investigate stellar and gas kinematics of 219 S0s in the SAMI Survey to look for signs of multiple formation pathways occurring across the full range of environments. We identify a large range of rotational support in their stellar kinematics, which correspond to ranges in their physical structure. We find that pressure-supported S0s with v/σ below 0.5 tend to be more compact and feature misaligned stellar and gas components, suggesting an external origin for their gas. We postulate that these S0s are consistent with being formed through a merger process. Meanwhile, comparisons of ellipticity, stellar mass, and Sérsic index distributions with spiral galaxies show that the rotationally supported S0s with v/σ above 0.5 are more consistent with a faded spiral origin. In addition, a simulated merger pathway involving a compact elliptical and gas-rich satellite results in an S0 that lies within the pressure-supported group. We conclude that two S0 formation pathways are active, with mergers dominating in isolated galaxies and small groups, and the faded spiral pathway being most prominent in large groups (1013 < Mhalo < 1014).