Were the reformers of the late 19th century and feminists of the early 20th century one in the same? Explain?

The short answer to your question is "yes". The feminist movement began with a group of reformers who saw that women were treated differently under the law and wanted to reform the legal status of women under the law.

The women of the late 19th Century attended an organized feminist gathering in 1848 at Seneca Falls, New York. John Stuart Mill brought the subjection of women to light in his work titled "The Subjugation of Women". Many women in the late 18th Century were jailed for being involved in the Women's Movement.

Women's issues ranged from voting rights, divorce rights,  labor rights, and rights to family planning and birth control. Notable feminists of the 19th Century were: Emma Goldman, Elizabeth Cady Stanton and Margaret Sanger.

The feminist movement in Egypt gained ground in 1899 in a book written by Qasim Amin, the author of the 1899  Women's Liberation (Tahrir al-Mar'a). In his book, he criticized some practices regarding the treatment of women in the Arab world as un-Islamic.

In the United States, Woodrow Wilson's 14 points helped the women's movement gain ground in the rights of self-determination. These 14 points propelled the states toward granting women the vote and right to property.

During the 1920s women lost the jobs that they had previously held during WWI. The pendulum swung back during WWII when the iconic "Rosie the Riveter" was the image of the woman who went to the factory while her husband went off to war.

After WWII ended, women were more reluctant to leave the workplace and go back into their homes and be good domestic partners. Socialistic and Communistic philosophies furthered the cause of feminist movements by holding up the cause of the "worker". Women had learned to be wage earners as well as housekeepers.

Eleanor Roosevelt, wife of Franklin D. Roosevelt,  was awarded a posthumous Nobel Peace Prize, the Norwegians refused and she was never so honored. In 1968 she was awarded one of the Human Rights Prizes. Mrs. Roosevelt did more as First Lady during the 1930s and 1940s to advance the cause of women, but she stopped short of supporting the "Equal Rights Movement".

The battle cry of the 1970s feminist was "equal pay for equal work." During the 1940s women had proved they could do any job that a man could do, but they were paid less than men were typically paid for the same job.

During the 1960s and 1970s women had access to modern birth control that was more reliable than any previous birth control method. Public education and family planning freed women from their roles as wife and mother.  However, the turbulent 1960s and 1970s also accelerated the rise of single parent families often with a female head of household.

So while women had more freedom, rights, and access to reproductive health care; the plight of women regarding their ability to advance economically has not progressed as much as many feminists would like.