Booker T. Washington and W.E.B. Du Bois were famous African-American leaders around 1900. Both men had different ideas regarding how African-Americans should get equal rights.
Booker T. Washington believed African-Americans should focus on getting their economic rights before focusing on getting their political rights. Booker T. Washington believed that African-Americans should secure their financial position first. He believed African-Americans should get vocational training to help them get good jobs. After their economic position was secured, then African-Americans should focus on getting their political rights. This idea was known as the Atlanta Compromise.
W.E.B. Du Bois believed African-Americans should insist on getting all of their rights at the same time. W.E.B. Du Bois believed there was no reason to delay getting any rights whether they were economic or political. He believed the struggle for equality was one that included getting all rights at the same time.
Both men wanted equality. They had different views about and approaches to getting full equality for African-Americans.