What do Sheol, Gehenna, and the final judgment actually mean?

Part of a series: questions that make more sense when the Tanakh and the New Testament are read together.

Sheol, Gehenna, and “the lake of fire” get flattened into one word — hell — more often than the text itself flattens them. David expects deliverance from Sheol, not an eternity in it (Psalm 16:10); Yeshua names Gehenna as a real, specific threat (Matthew 10:28); Revelation describes a final judgment by what's written in the books (Revelation 20:11–15).

What does each term actually name, and where do they overlap? Bring your sources.