This question might seem basic, but how does one conclude that the Klein-Gordon equation describes spin zero particles but Dirac equation describes spin half particles. Thanks.
EDIT: Adding more details
One can derive both equations from the relativistic energy-momentum relation.Moreover, Dirac equation is just the linearization of the Klein-Gordon equation, and since both equation come from the same "source" how can both describe different things? is there something special about the linearization process? Also how does one know that a certain equation describes a certain type of particles is there a theoretical justification for this conclusion or just experimental? I am just starting to learn about these things and I am confused to how people came to these conclusions.