What did the North and South want during the Civil War?

The North wanted to abolish slavery while The South wanted to continue slavery.

Not quite. The south didn't want anything persay. The cicil war is often catagorized as being a war over slavery, and this is false. The north was fighting to keep the union in tact. Abraham Lincoln stated that "If (he) could save the Union without freeing any slaves I(he) would do it, and if (he) could save the Union by freeing all slaves, (he) would do it....What (he did) about slavery, and the coloured race, (he did) because (he believed) it helps to save the Union."

The south was fighting the was as a constitutional issue. They felt that the abolition of slavery and the compromises of 1850 and the Missourri Compromise impeded on their 10th amendment right to decide for themselves.