Basically, the relationship between these two movements is that the abolitionist movement helped lead to the women's movement. The reason for this is that many women were involved in the abolitionist movement. These were women like Elizabeth Cady Stanton, Lucretia Coffin Mott, and the Grimke sisters. As these women fought for the rights of African Americans, many of them came to think about their own lack of rights. It seemed to them that it was ironic that they would be helping to try to secure for African Americans rights that they themselves did not really have. This helped lead to the calling of the Seneca Falls Convention in 1848, which is seen as the start of the women's rights movement.
There was a direct relationship between the abolitionist and women rights movement, however, it should be noted that this relationship was not a simple one. The relationship between the two movements was born of necessity because the groups both suffered from oppression. The women rights groups knew how to organize themselves from the abolitionist movement. They knew of political tactics to create awareness and pressure the leadership into recognizing their rights. Leaders of the women rights movement knew of such tactics when they were active participant in the anti-slavery movement, but due to oppressive treatment by the men in the abolitionist movement, the women decided to forge their own movement to champion for their rights. In some ways, women realized that by supporting the abolitionist movements they would in turn force the administration to address their own issues as women, and also earn support from some of the men in those movements such as Frederick Douglass.