What have historians called some of the empires that existed in the nineteenth century prisons of nationalities and what empires were they referring to

It sound like you are talking about the European colonial empires. Britain, France, Portugal, Germany, Italy and Belgium formed empires by conquering lands in Africa, the Americas and Asia and turning them into colonies. Spain had created the oldest colonial European empire in South and Central America and the Philippines , but lost it in the 19th century.