There is a great deal of confusion between these sexism and misogyny.  I myself confuse them on occasion.  This does not stop me from being annoyed when ever I see the words misused.  These are two very distinct words with very distinct meaning and very distinct connotations.  They are very different concepts.  Sexism and Misogyny are not interchangeable.  They are not even synonyms.

Merriam-Websters defines misogyny as:

a hatred of women

Merriam-Websters defines sexism as:

behavior, conditions, or attitudes that foster stereotypes of social roles based on sex

Supporting stereotypical social roles based on sex is not hate.  It is traditionalism.  I didn’t hate my mother for cooking dinner or doing the laundry when I was a child.  I don’t hate her for not doing these things for me now.  Supporting traditional gender roles is advocating for what a system that you believe is best for everyone.  Believing that women really will be happier barefoot pregnant and in the kitchen isn’t hating women.  It is loving women, wanting what is best for them.

For men, the people most often accused of misogyny when it’s really sexism, the two are incomparable.  The stereotypical social role of men is provider and protector.  You kill people you hate, or at least avoid them and hope the get hit by a bus.  You don’t buy them pretty things, provide them with food and shelter.  You most decidability don’t put yourself in harms way to protect something you hate.  You cheer the oncoming bus, you don’t pull them out from in front of it.  Sexism and misogyny are incomparable.

Sexism is much more common than misogyny.  Real misogyny is very rare, much more rare than misandry.  Lets do examples.

“Women should be barefoot pregnant and in the kitchen”

This is sexism.  This is not misogyny.  It is a traditional gender role, not hate.  Women not barefoot pregnant and in the kitchen are destroying America is hate.  I think “Should be” and “are destroying America” is a rather clear distinction.

“Men are not good with kids”

This is sexism.  This is not misandry.  It is a traditional gender role of man breadwinner, woman care taker.  Children are in danger around men would be misandry.

Just a randomish rant.  This is just something I see a lot of and it bugs me.