Historically, an orphanage is a residential institution, or group home, devoted to the care of orphans and other children who were separated from their biological families.

What is the difference between a private and public orphanage?

is that public is the people in general, regardless of membership of any particular group while orphanage is a public institution for the care and protection of orphans.

Are private orphanages a thing?

While there are still many children in need of permanent adoptive homes, today's domestic adoptions no longer involve traditional orphanages. Instead, U.S. orphanages have been replaced with an improved foster care system and private adoption agencies like American Adoptions.