Both filter systems pass non-image forming lite as an aid to seeing the image when dodging and burning. The Ilford system passes red light (the color of a red safelight), the Kodak system passes orange light (the color of an 'OC' safelight). Kodak filters are lighter and have an orange tint to them when compared to Ilford filters.
You can use Kodak filters with Ilford paper but the contrast grade will be a bit different from that produced by the Ilford filters. When used with Ilford paper, Kodak filters won't produce the same 'constant exposure for ~1.0 OD' that Ilford filters produce.