The NWSA emerged from a split in the American Equal Rights Association. The other emergent group was the American Woman Suffrage Association (AWSA).
Susan B. Anthony, and Elizabeth Cady Stanton opposed the Fifteenth Amendment, demanding that the amendment include women's suffrage. They in turn founded the NWSA based upon a belief that a federal constitutional amendment was the best way to achieve their goals. The AWSA pursued state-by-state changes.
The two organizations eventually merged in 1890, to form the National American Woman Suffrage Association(NAWSA).