Panoranic refers to the degree the angle over which the image is captured, angle over which the scene is captured in the image by the camera. So here for example is a 360° degree captured, all around for a fixed height over a certain height, a certain visual angle vertically the scene is captured all around in this sense. But this is the part that the panorama, that panoramic refers to.
Omnidirection refers to imaging in all directions. So ideally an only direction a camera would be seen along all directions that define a sphere.