Christina Hoff Sommers is the author of the distinction between gender feminists (radical misandrists, cultural Marxists, etc.) and equity feminists (those who seek equal opportunities for women and men, like Sommers herself). As far as I know she introduced the concept in her 1995 book Who Stole Feminism?
I won't summarize the book too much here. Sommers did a lot of serious debunking of leftist horror stories about mistreatment of women, from rapes in college to beatings in the home to unfair wage gaps in the workplace. Her main thesis is that gender feminism is not based on facts, it does not believe in or seek equity between men and women, and it does not improve the situation for anyone (except tenured gender feminist academics). In contrast, equity feminism is what is good and and true, is as American as apple pie, and still enjoys healthy support among ordinary women (though it is somewhat underrepresented on certain campuses).
As a doctrine which both infantilizes and deifies women, gender feminism can naturally be criticized from several angles. Sommers tends to doubt the notion of "women's ways of knowing" which gender feminists have used to insulate themselves from criticism that their conclusions are asserted rather than proven, and developed using emotional feedback in committee settings rather than using facts. Sommers is dead on, but I think she pays too little attention to the possibility that women do think differently from men.
I wouldn't go so far as to consider myself an equity feminist. I'm a heathen formalist of the hard right. I don't "believe in equality" so much as I advocate single standards. Still, I see little that distinguishes my political positions from those espoused in the book. Women may or may not process data differently from men (I think they do), a few may be able to succeed in virtually any occupation (I think they can), or maybe just as many women can succeed in a given high-power job as men can (I doubt it).
The bottom line is: as long as discussion is open and honest, and as long as the system is rich in single standards, any decent civilization can accommodate ambitious women. The problem with feminism is not biological but ideological, and therefore transient. Brave men and women can stand up to the genderfem/ cultural Marxist/ PC threat, particularly if they have a position at the American Enterprise Institute.
(Coming up: Strange, out-on-a-limb thoughts connecting feminism and white nationalism. Be patient; my baby boy takes a lot of time.)