Recently someone told me that racism means that it means both race and gender discrimination. However, I think that sexism is the word used for gender. Am I correct?
You definitely wouldn't use 'racist' for anything to do with sex-based discrimination. You could say that such a person was being sexist, or you could say that they were a chauvinist (though that generally refers to when someone believes that their sex is superior to the other).
'Racism' is somewhat like chauvinism, in that it is generally used to express the idea that "my race is better than your race (or all other races)". The slippery point here is the definition of 'race', which many often extend to include things like religion, which of course isn't a 'race'.
'Bigotry' is a better term to describe someone who is intolerant of other peoples' religions, or their belief systems in general.
To sum up these intolerances:
- If it's gender-based, it's sexism or chauvinism.
- If it's based on physical characteristics, it's racism.
- If it's based on ideas or beliefs, it's bigotry.
In general, racism relates to race: phrases like "racist against Christians", though well-attested, are not well-accepted. Pure gender discrimination, with no racial element, is therefore unlikely to be considered "racism".
However, racism often has very specific interactions with gender stereotypes — for example, black women in the US are often presented as being less feminine than white women — and these are usually considered to be, first and foremost, forms of racism (rather than of sexism).