I will add to Leauki's with the following. A racist is one who believes that a race is inferior by the race itself. Beyond the obvious differences (different colors). A racist is one who will not tolerate those that disagree with them in the same race. They think that all of one race must believe as one. A racist is one that believes that inferiority is based upon the race (or superiority), and who then goes and practices that. Such that they cannot accept one of their race being something they cannot fathom.
40 years ago, about the only racists were caucs in this country (USA). Today, there are still cauc racists. But more and more, there are racist of every color. They do not tolerate those within and without their race that do not kowtow to their beliefs. never understanding that very few people are of one pure race. They denigrate another or their own race based upon, not the words or beliefs of the person, but on their perceived idea of what that person should or should not believe.
Racism is not defined by who you hate, but how you hate. And that corrals a lot of people all over the spectrum.