The Homeric poems were being codified around the 8th cent. Of Zeus' children born of mortal women, only Dionysos and Herakles made the cross over to godhood. Asclepius, son of Apollo, is the other rare exception. A banquet is held in their honor. One very important difference between heroes and gods is that the hero is always confined to a specifc locality.
Gods can move freely about.
However, there are stories of heroes being transported from one place to another. But there power is still limited to that locale. Historical persons could become heroes as well. In addition to ones you will read about below and in the readings, the founder of colonies would frequently become the heros Ktistes and buried in the market place. Other heroes are recognized after the ghost haunts or curses a community.