The difference between Josiah Mason's Orphanage and the workhouse surely is that the children who were given shelter in the orphanage had no family. The children who were in the workhouse had family although they were separated from them, and there were girls and boys schools on the plan of Dudley Road Workhouse posted by Judy.
I have only just read your comments so am just replying with small bit of information !
My dad, Sidney Smith was in the Orphanage after his father was killed in the first World War - his brothers were placed in the Blue Coat School leaving his sister at home with his mother in Aston. She had no means of supporting the children. He hated it and told me that they only had decent clothes on Sundays to go to church. He said they had to crawl under fences to neighbouring fields to pinch the cabbage stalks to eat as they were so hungry. It certainly affected him, as though he was a decent man, he could never show emotion. I don't think it was too nice a place and certainly he had family so it was not just for orphans it seems.