They both want to kill somebody. Claudius wants to kill Hamlet; Hamlet wants to kill Claudius.
Claudius
Claudius was hamlets Uncle and later became his stepfather because his mother Queen Gertrude married Hamlets uncle "Claudius".
Claudius
Claudius
King Claudius, who also happens to be hamlets uncle.
Horatio
Claudius killed him.
Gertrude, Hamlets mother.
Claudius
If this is Claudius in Hamlet, its because he killed hamlets father to take the thrown.
to become king
Hamlet's Uncle Claudius