class is used these days synonymously with a big group of people (and maybe has been for a long time in science? thinking of plant classes? eh), but even now it is more about describing people who have some distinguishing thing in common (class of women, the working class, etc).
mass is more undifferentiated, so it's an even more egregious generalization.
but in the sense that both are absolutely based on generalities, and presume that people can make decisions and assessments based on almost-no or no information of Other People, your question's premise is correct: there is no/very little difference.