These two things are linked at the hip any way you slice them. Racism is a form of discrimination which is based upon race. Discrimination has perhaps broader application and can apply to more than race, but the effect is the same. Both are terrible, and closely related, concepts. Both can represent both actions and beliefs.
Racism is just a particular type of discrimination. Therefore, one cannot be "better" or "worse" than the other. I'm sure there are some people, however, who might believe that there's a difference between the two words. One might say that discrimination is the action or behavior, racism is just the mindset. (Some might suggest it's vice versa). I personally believe that racism can be both a mindset and an action. Whether one acts on his or her bigoted feelings or just has a particularly negative mindset towards other groups, that person is still discriminating. By the very process of selecting one group and deeming them to be lesser or better than another group automatically reflects discriminatory notions, regardless whether they're acted upon or not.