Heraclean and Herculean mean precisely the same thing. How could it possibly matter which you choose to use? Which DO YOU choose? Why?

Well one killed the Hydra.   Hera was the wife of Zeus.  Hercules was the son of Zeus and a mortal. 

Oh wait.  WAIT WAIT.  YOU ARE RIGHT. 


Heracles (/ˈhɛrəkliːz/ HERR-ə-kleez; Ancient Greek: Ἡρακλῆς, Hēraklēs, from Hēra, "Hera"), born Alcaeus[1] (Ἀλκαῖος, Alkaios) or Alcides[2] (Ἀλκείδης, Alkeidēs), was a divine hero in Greek mythology, the son of Zeus and Alcmene, foster son of Amphitryon[3] and great-grandson and half-brother (as they are both sired by the god Zeus) of Perseus. He was the greatest of the Greek heroes, a paragon of masculinity, the ancestor of royal clans who claimed to be Heracleidae (Ἡρακλεῖδαι), and a champion of the Olympian order against chthonic monsters. In Rome and the modern West, he is known as Hercules, with whom the later Roman emperors, in particular Commodus and Maximian, often identified themselves. The Romans adopted the Greek version of his life and works essentially unchanged, but added anecdotal detail of their own, some of it linking the hero with the geography of the Central Mediterranean. Details of his cult were adapted to Rome as well. This post was edited by WM BARR . =ABSOLUTE TRASH at August 15, 2017 8:38 AM MDT

One for the classical scholars. I've always used the latter. 

Would you settle for a Wine God?

I think Hercules is hotter.