Dang Reality! explains the difference between what liberal feminists say about radical feminism and reality.
Liberal feminists say that in order to support women in patriarchy we must not examine their personal choices from a political perspective. Radical feminists say, why not both? We try to refrain from judging women for participating in patriarchal acts (for example, I’m a makeup artist and a radical feminist at the same time) and we recognize that women do what they must to survive in patriarchy, however we do not pretend that those behaviors are feminist just because they make us happy or benefit us in some way. For example, getting married can be awesome and fulfilling and if that’s what you want then awesome, no one is stopping you, but that doesn’t change the fact that it is literally the cornerstone of patriarchal society.
Generally speaking radical feminists believe that no part of your life is free from societal influence, and therefore no part of our lives should be free from feminist analysis. This can be summed up to “the personal is political.”