Wreak is the verb you want before 'havoc' or 'revenge' — it means to cause or inflict something damaging. Wreck can be a noun for the wrecked thing itself, like a shipwreck, or a verb meaning to destroy something. The storm wreaked havoc on the coastal town, and that havoc wrecked several boats in the harbour.
The core difference
Wreak means to cause damage, while wreck means to be, or to become, the damaged result.
- wreak — to cause or inflict something damaging or violent, such as havoc or revenge: The storm wreaked havoc on the coastal town.
- wreck — the ruined remains of something destroyed, or the act of destroying it: The crash left the car a total wreck.
How to tell them apart
The fixed phrase "wreak havoc" trips people up most, since many writers reach for "wreck havoc" instead. But havoc is what gets caused, not what gets wrecked, so wreak is the correct choice there.
Both words share an Old English root meaning "to drive" or "to punish," which is why their meanings sit so close together. A simple check: if you are describing the damaged end result — a car, a ship, a person's nerves — use wreck. If you are describing the act of causing that damage, especially in the set phrase "wreak havoc" or "wreak revenge," use wreak.