It’s not uncommon to use the words “sexism” and “misogyny” more or less interchangeably, or as if the latter is just a more extreme version of the former. But Kate Manne posits that in fact these are different systems which collaborate effectively together. Firstly,
misogyny should be understood primarily as the “law enforcement” branch of a patriarchal order, which has the overall function of policing and enforcing its governing norms and expectations.Manne, Down Girl, page 78
sexism should be understood primarily as the “justificatory” branch of a patriarchal order, which consists in ideology that has the overall function of rationalizing and justifying patriarchal social relations.Manne, Down Girl, page 79
What I find especially useful about this disambiguation is that it permits a great deal more specificity and clarity about events, whether public or personal. E.g.: if someone asserts that women just aren’t that good at math, that’s sexism. But if they then exert their influence over a university hiring process to refuse a qualified woman for hire because she seems too “entitled” or “aggressive,” that’s misogyny in action.
On this picture, sexism will tend to discriminate between men and women, typically by alleging sex differences beyond what is known or could be known, and sometimes counter to our best current scientific evidence. Misogyny will typically differentiate between good women and bad ones, and punishes the latter. Overall, sexism and misogyny share a common purpose—to maintain or restore a patriarchal social order. But sexism purports to merely be being reasonable; misogyny gets nasty and tries to force the issue. Sexism is hence to bad science as misogyny is to moralism. Sexism wears a lab coat; misogyny goes on witch hunts.Manne, Down Girl, page 79
This is also instructive, inasmuch as misogyny’s nastiness can provide cover for more polite sexism. Maybe a report of a woman politician won’t pay lip service to the more gross allegations that swarm around her, but the same report will be more than happy to note that she seems a good deal colder and more distant than her male opponent. Sexism and misogyny then get to play good cop and bad cop, with gallant sexism off the hook in comparison to misogyny’s more brutal nature. In either case, though, the deed is done: a woman is put back in her place.