I agree entirely with your main point, but I think it’s worth noting that many actual feminists are unfairly painted as misandrists. I write a lot about women's issues and feminism, and I always get at least one response from some dude asking me why I hate men. These people know that feminists don’t hate men, but they’re trying to silence us with ad hominem arguments. If we’re “hysterical man-haters,” we can’t be taken seriously. So they are quick to dismiss us as misandrists even if we’re promoting equality. I’ve even had people accuse me of misandry when I was actually writing about how intimate partner abuse affects men.
That said, there are certainly women who do hate men, and I recommend calling them out if they identify as feminists. In my experience, such “feminists” tend to be TERFs and SWERFs as well, so they’re excluding a lot of people from their pursuit of “equality”!
I think it’s important to draw a distinction between the two words, but more important to recognize that people are conflating the two for political purposes, not out of confusion.