My 4E lore is admittedly rusty, but my understanding is that the natural world is "based in the elements" only in that the Material Plane is where the Elemental Chaos intersects with the Astral Sea - it is the realm where the two overlap, as much "Elemental" as it is "Astral".
The Primordials are explicitly Elemental beings, while the gods are explicitly Astral in nature, and the lore as I recall it portrays both as fundamentally extraplanar forces.
The Primal forces - druidic magics, wild gods, etc. - are, by contrast, explicitly of the Material Plane, and came about as the natural world's response to the devastation of the Dawn War, effectively the world reacting to the rampant destruction caused by the Elemental and Astral powers in their fight over the Material Plane by creating its own powers to kick them both out.
There may be a great deal of visual and thematic overlap between a primordial elemental storm entity, a primal storm nature spirit, and a storm god like Zeus or Thor, but fundamentally they are all members of different cosmological "teams".