Not quite - Hillman and Commer where two divisions of the same parent company.
In this case the parent was Rootes Group, within Rootes Hillman, Humber, Singer, Sunbeam and Talbot, produced cars. Where Commer and Karrier were both commercial vehicle arms.
The company has now disappeared and is in someway part of Peugeot know.
As an aside one of the last models made was a Talbot Sunbeam now there is a confusing name for a car...