Put very simple: once the swiss Tellko and the british Ilford merged under the ownership of Ciba under the Name of Ilford. But that was also the time of Cibacolor. In the beginning crisis they split with the swiss entity going on as Ilford Imaging, whereas the british entity re-started as Harman.
With Harman making b&w films and paper, Ilford Imaging making colour films and paper. Both also make ink-jet papers.
Ilford Photo is no company, not even a department as Simon indicated above, but only a manufacturer brand of Harman, designating part of the Harman-made silverhalide materials.