There were a lot of similarities, and differences. The women's movement was more likely white middle or upper class women to begin with, the Civil Rights movement, of course was primarily African Americans but also whites were involved.
The Women's movement started with the suffrage movement, to get women the right to vote and that happened in 1919, I believe.
Women were somewhat quiet over the next 40 years or so, of course during WWII, many women worked in factories, etc. but there was no 'women's movement", just a need for workers, after the war things went back to 'normal' with women at home raising kids and cooking dinner. (In, according to TV perfectly kept houses while they were in dresses and pearls and high heels)
By the 1960's, the civil rights movement was inspiring a lot of other groups, including Latinos, women and eventually Gays.
Women who were in the lead were not fighting poverty for the most part, at least for themselves. They were often from middle class families but were well educated, but a woman at the time could go to college, get a degree and work as a teacher or secretary until she got married. Then it was over. Unless her husband died, or she became one of the ever growing number of divorced women, she probably would not work or use her degree or experience.
I was young at the time, but I do remember as late as the 60's, at least one family where the husband refused to let his wife drive, because he did not like "women drivers". This woman and at least one other did not vote, because 'that was something for men to know about' (I'm talking 1960's, not 1860's!)
The Civil Rights movement was more extensive among many classes of African Americans. While there were many educated and middle class Blacks involved in the leadership, it included the poor to a great extent. There was probably more support for Civil Rights among the grass root African Americans than for the Women's movement among a lot of white people, even women. Many thought they were either 'kooks', or some thought they were either all lesbians, or that they were ' too ugly to get a man', even though many were married women.
Hope this helped.