I was a little surprised at how much discussion took place on Facebook yesterday when I mentioned that the "gates of hell" in Matthew 16:18 were not the gates of Gehenna, the hell of fire, but the gates of Hades, the gates of the dead.
I suggested that Matthew's audience would have immediately associated the "gates of Hades" with stories they had heard ranging from Odysseus to Hercules. The realm of the dead in that frame of reference did not distinguish between the righteous and unrighteous but had all the mindless dead mixed together.
Then someone mentioned underlying Aramaic. We didn't go down that rabbit hole (For example, is there an underlying Aramaic for this verse in Matthew?). But in Hebrew/Aramaic, there was still a distinction between Sheol as the general realm of the dead and Gehenna as a place of fiery destruction.
To sum up the main words (e.g., I've left out abaddon):
Sheol: The Hebrew word for the realm of the dead. The OT has no concept of an eternal place of punishment (Dan. 12:2 comes closest). Sheol is basically a poetic way of referring to the realm of all the dead. "He will not abandon my life to Sheol" in Psalm 16:10 originally meant, "He will not let me die."
Hades: Hades is the Greek equivalent to Sheol and also does not distinguish between righteous and unrighteous. It is a way of referring to all the mindless dead. The gates of hell will not prevail against the Church means that death will not prevail against the Church.
Gehenna: The Aramaic word arose in the late intertestamental period in reference to the trash heap outside Jerusalem in the Valley ge Hinnom. It was thought to be the place where the bodies of the dead would be burned after an apocalyptic battle and thus came to be used in reference to the place of eternal fire for the ungodly. It occurs primarily in Matthew.