Nelson Mandela and Steven Biko both believed in ending apartheid and bringing about civil rights and legal equality for black citizens of South Africa. They both believed that such a social revolution could be achieved non-violently, but both were willing to fight if it came to that.
Mandela was affiliated with the African National Congress, which did have a militant/violent sect but believed if enough popular pressure could be brought to bear on the South African government and that if it could force Mandela's release from prison, then the rest of the revolution could be won easily.
Biko believed that all that was needed was to raise awareness of black culture and identity, to give them pride in who they were and a sense of equality within themselves. He called this "Black Consciousness" and believed that once blacks became aware of their own worth as human beings, they would no longer tolerate living under apartheid and a widespread revolution could not be stopped.