Both the parties had released their intent, which changed the behavior of the energy around them. Jake's understanding about intent was shallow, but he did know that it wasn't a form of energy. The concept behind it was different. It could be understood as a form of inducing awareness into the energy itself to make it more effective in a manner desired by the individual.
That was the reason the system graded the intents into different groups. There was a separate section for fist, spear, sword and everything else to which the intent can be applied to. To understand it in a more detailed manner, one could say that the usage of energy in each of these areas differ in generation, circulation, application and manifestation. That is why there was a segregation between sword and saber intent. They are having the same root of genesis and the same route of application, but they differ on a fundamental basis.