I am currently reading a book called A Labyrinth of Kingdoms by Steve Kemper which details the expedition of Heinrich Barth through Central Africa. The book repeatedly refers to their travel through "Soudan" which is current day Niger and Nigeria. I am wondering why this namesake instead came to represent the present day area south of Egypt. I also found a map from 1850 which seems to follow the same premise.
Sudan comes from Bilad as-Sudan ('land of the blacks'), which was the general term in Arabic for the belt of Africa between the Sahara and the forested lands farther south. The name continued to be used for various territories in this region well into the 20th century. In the east, there was the Anglo-Egyptian Sudan, which became the Sudan that we're familiar with. To the west, the French administered their own Sudan, the territory of which eventually corresponded to that of present-day Mali.
The Anglo-Egyptian Sudan gained independence as the 'Republic of the Sudan' in 1956. By 1958, French Sudan had become the 'Sudanese Republic,' part of the French Community. The Sudanese Republic and Senegal united as the Federation of Mali in 1959, remaining part of the French Community. This union negotiated its full independence from France in 1960, Senegal promptly withdrew from the federation, and the Sudanese Republic decided to stick with 'Mali', leaving the world with only one Sudan.
The place name "Sudan" comes from the Arab phrase Bilad al-Sudan (trans "land of the blacks"). This phrase was used edit: from about the 11th century onwards to refer to areas of Africa on the Sahara's southern edge, which would include areas from Takrur in what is now Senegal to Dar Fur and the Nubian states in what is now the Republic of Sudan. Sometimes, western geographers and scholars will sudivide this broad area into the Western Sudan, Eastern Sudan and occasionally the Central Sudan (in the region around Lake Chad).
When the French and British empires extended their influence in Africa in the last quarter of the 19th century, the French often referred to their holdings in West Africa as Soudan.
Now, from the 1820s until 1881, the Khedives of Egypt extended their influence into the upper reaches of the Nile (what is now Sudan and South Sudan), and styled themselves as the Wali Sudan. In 1881 the Mahdist revolt broke out against this Egyptian influence, and Britain became drawn into the war. After victory in 1899, Britain ruled the region (nominally with Egyptian co-rule) as the Anglo-Egyptian Condominium of Sudan.
So, while your map from 1850 shows a European understanding of the region as Nubia, the Mahdist revolt and then the Condominium brought the Arab/Egyptian geographical conception of the region as part of the Bilad al-Sudan into the English lexicon.
To demonstrate, compare this book from 1862 which uses the term Nubia for the region, with this one from 1891 that talks about the Egyptian Sudan.
