Sexism is socially systemic sexual discrimination.
Racism is socially systemic racial discrimination.
Classism is socially systemic class-based discrimination.
This is why you'll find people who say "You can't be sexist against men." You can obviously discriminate against a man based on sex, but that's not part of a larger, overarching societal norm. When the discrimination becomes routine, ingrained, and pervasive, that turns it into an 'ism.'
Racism is socially systemic racial discrimination.
Classism is socially systemic class-based discrimination.
This is why you'll find people who say "You can't be sexist against men." You can obviously discriminate against a man based on sex, but that's not part of a larger, overarching societal norm. When the discrimination becomes routine, ingrained, and pervasive, that turns it into an 'ism.'