Throughout the twentieth century many have taken up the fight against racial discrimination and oppression, and demanded equality. Multiculturalism is different. Its central thesis is not the overcoming of inequality, but the accomodation of inequality. Multiculturalism takes difference, not equality as its starting point (and its conclusion).
The other central difference between multiculturalism and anti-racism is that multiculturalism is for the most part an official discourse operated by teachers, municipal administrators, human resources managers and government officials. Anti-racism was for the most part a set of struggles against the state.
Multiculturalism has coopted the anti-racist struggles of the past into its imaginary history. At my school, teachers will happily tell my daughter about Claudia Jones in Black History Month. (And in the next breath they invite her to join the Metropolitan Police run 'Detective Club'.)