To blame someone is simply to accuse someone. To blame someone you just need to say they did it. However, guilt requires proof. There needs to be evidence.

First of all "blame" is used as both a noun and verb, while guilt is just a noun. "blame" as noun means a criticism, accusation, or complaint people attribute to someone for a bad outcome (they put the blame on me). "guilt" is the an uncomfortable and uneasy feeling one has after doing something bad or causing others pain. It is a burden one has in one's mind about one's wrongdoing. In law it means culpability, a determination that one has committed a crime, violation, or wrong.