Studies of these churches generally sort them into streams, and the sorting is worth knowing because the label covers bodies with very little in common beyond their independence.
The first stream is usually called Ethiopian, a name taken from the verse about Ethiopia stretching out her hands to God rather than from the country. These churches separated from mission bodies over control rather than over doctrine, keeping the liturgy, the confession and often the name of the parent church while insisting that Africans should lead it. The earliest date from the late nineteenth century in South Africa and West Africa.
The second stream is prophet-healing, and it is much the largest. These churches were founded by a person who received a call, and they centre on healing, prophecy, dreams and the direct action of the Spirit. The Aladura churches of Yorubaland, the Zionist and Apostolic churches of southern Africa, and the Kimbanguist church of the Congo all belong here, though they arose independently of one another.
A third stream is often distinguished for churches whose practice draws more heavily on ritual purity, uniform and hierarchy, and there is real argument about whether it is a separate type or a variant of the second. What the categories are for is comparison, not classification for its own sake, and every scheme in the literature has churches that sit awkwardly across two of its boxes.
Sources African Reformation: African Initiated Christianity in the Twentieth CenturyAllan H. Anderson with Bantu Prophets in South AfricaBengt G. M. Sundkler, Aladura: A Religious Movement Among the YorubaJ. D. Y. Peel, Kimbangu: An African Prophet and His ChurchMarie-Louise Martin