Platonic pursuit is a moral code while Platonism is a philosophical code.
Explanation:
Platonism can be one of or all the various entities of philosophy derived from the work of Plato and his various writings. This may include neo-platonism movement of late or the original school of Plato where his influence was in Greece.
The Platonic Pursuit is a moral code through which one can find a way to philosophical pursuits and pursuit of happiness which is a concept later derived from this pursuit of Platonic ideals.