The term capital murder is usually used by states that still have the death penalty. Capital murder is a crime that warrants the death penalty, such as a serial killing or a really heinous crime. First Degree murder means the murder was intentional but the prosecutor is not seeking the death penalty.
Capital murder also means you killed someone while in the commission of another serious felony such as another murder, arson, kidnapping, etc. In some states it also applies to the killing of children, elderly, and mentally disabled.