I suppose that the main difference in philosophy that is causes the split between the two groups is their assessment of why women are discriminated against and oppressed.
I am going to explain this very poorly but:
Lib Fem: women are discriminated against and have their choices and autonomy limited in a patriarchal society (why? because they are women? Because patriarchy? I feel like I used to know this but it now escapes me!) feminism is about creating equality of opportunity for women to participate in society on the same basis as men. It is about empowering individuals and validating women's choices. It can become a sort of philosophy where anything a woman does is feminist because she is a woman and she chooses it. Generally believes in intersectionality in a way that creates hierarchies of oppressions and believes that trans women are women because they identify as such and have the same or worse problems as women. Believes that pornography and sex work can be empowering for women if that individual chooses. Believes that sex and gender are not the same and that gender is about how you present yourself and is changeable based on your inner feelings. Believes in subverting gender by being gnc, non binary or trans.
Rad Fem
Borrows a lot from Marxist class analysis. Believes that women as a class are oppressed by men as a class because of their biology. Because men want to control women's sexual, emotional and reproductive labour.
Believes that choice is an illusion within an oppressive societal structure because it ignores the ways in which women's choices are limited by the structures of a patriarchal society. Believes that porn and sex work are inherently violent against women and exploitative.
Believes that sex and gender are different but views gender as a hierarchy with men on top and women on the bottom. Believes that women are conditioned from birth to take the subservient and care taking position in the hierarchy so that men can utilise their labour. Believes that the only differences between men and women is biological fact (that women bear children) but reject the idea that women are inherently more submissive, caregiving, like makeup, dolls and high heels because they are women.
Reject the idea that men can become women because they identify with femininity as they understand that the source of women's oppression is biology.
2nd wave refers to the women's lib movement of the 1970s and is generally used as a synonym for rad fem although not all second wavers were rad fem.
3rd wave refers to the current feminist movement since maybe the mid-late 90s? It is often used as a synonym for lib fem.
The thing is that liberal feminism is easy. You can pretty much do what you want as long as you can think of a way to justify it and it doesn't discriminate against anyone else. Rad fem is much scarier as you really have to analyse your choices and realise how much they are affected by patriarchy and your socalisation.
I recently had a bit of a lightbulb moment and made the switch but I am not particularly well informed or well read which is why I started the book club thread. Come and join us!