The difference between capital murder and first-degree murder is that the killing in a capital murder case has an additional factor or circumstance for which the punishment is more severe. Basically, capital murder is first-degree murder plus one of these additional elements: 1. The murder was either extremely callous and cruel or 2. The murder was committed during the commission of another serious felony offense, or 3. There were multiple victims, the victim was a child under a certain age, or the victim was a peace officer or fireman.