The two conflicts are different and based in different issues.

The primary conflict over the previous decades was between the Sudanese government in Khartoum, which espoused an Arab-Supremacist and Muslim-Supremacist Policy and the South Sudanese tribes which were Black African Christians. That conflict did indeed end with the independence of South Sudan. (The Darfur Conflict/Genocide, which was caused for the same Arab-Supremacist reasons, even though Darfurians are Muslims, continued because Darfur is not part of South Sudan.)

The current conflict is a conflict between the two largest Black African tribal groups, the Dinka, who are the majority and represented by South Sudanese President Salva Kiir Mayardit, and the Nuer ethnic group. The Nuer feel that the Dinka-led government is working insufficiently to protect the property of the Nuer and so the Nuer are fighting for the preservation of their livelihoods. The Dinka-led government has attempted to protect Nuer rights, but has been attacked by the Nuer White Army in several incidents.