Nietzsche gives one take on this distinction, when he contrasts "good vs. bad" or "master" moralities with "good vs. evil" or "slave" moralities. An evil man is one with evil goals; a bad man is one who is inept at achieving his goals.

Another contrast is that if the Greeks or the Romans had been utilitarians, they would never have been average utilitarians, and I don't think they would even have been total utilitarians. They might have been maximum utilitarians, believing that a civilization's measure was the greatness of its greatest achievements and its greatest people. Americans must have at least briefly believed something like this when they supported the Apollo program.

(I must be overgeneralizing any time I am speaking of the morals of both Athens and Sparta.)

Classical Greek ethicists propounded values that were in many ways similar to modern ones. Ancient Greece is the time period in which works like the Illiad were put to writing, and those demonstrate some values that are quite foreign to us.