Prejudice is literally pre-judging someone or something--that is, forming a judgment before you have all the facts. Like in the title of Pride and Prejudice
, this pre-judgment isn't necessarily based on bigotry. Nevertheless, "prejudice" can be synonymous with "bigotry" and "discrimination."
Racism, broadly speaking, is prejudice based on racial bigotry. In a more technical sense, only systemic racial prejudice is classed as racism. So under this narrower definition, there is no anti-white racism in the US, even though individuals may be racially prejudiced against white people.