how is heroism today different from heroism back in the greek society?

Unlike our heroes of myth, everyday heroes are firefighters, cops, first responders. They are Dads and Moms, soccer coaches, the old neighbor down the street who watches your house while you work.

Yes and no- It is not different in that heroism in Greek society usually meant saving someone or doing renowned deeds, much like heroism today. It is different in that many heroes in greek mythology (actual real life?...*suspenseful music*...) were blessed with demigod abilities and they were slaying big bad monsters and all that good stuff. And many, if not most, heroes in Greek mythology were immoral, egotistical jerks that would kill you for touching them. Heck, the "gods" were jerks too- it was all one big Jerkfest back in those days!

A hero (from Greek ἥρως hērōs), in Greek mythology and folklore, was originally a demigod, the offspring of a mortal and a deity, their cult being one of the most distinctive features of ancient Greek religion.

Later, hero (male) and heroine (female) came to refer to characters (fictional or historical) that, in the face of danger and adversity or from a position of weakness, display courage and the will for self sacrifice – that is, heroism – for some greater good, originally of martial courage or excellence but extended to more general moral excellence.

Stories of heroism may serve as moral examples. In classical antiquity, hero cults – veneration of deified heroes such as Heracles, Perseus, and Achilles – played an important role in Ancient Greek religion. Politicians, ancient and modern, have employed hero worship for their own apotheosis (i.e., cult of personality).

you don't think "myth"olgy was real do you? However, I do think I know what you mean. Heroism is almost nonexistent due to the liberal idiots in our lives today. Try to be a hero today and some lawyer will try to sue you for it. I hate liberals.