I feel like I should clarify a couple of terms for all. After all, I did introduce the "wear ship" term into the fray.
I will use the original poster's clock analogy to provide the visual for the following definitions.
3. Wear Ship
4. Chicken Gybe
If we assume the wind is coming from 12:00 and you are sailing with the bow pointed at 2:00 you are close hauled on a port tack. If you were to swing the bow through the wind at 12:00 and end up closed hauled again with the bow now at 10:00 you have TACKED through the wind and you are now close hauled on a starboard tack.
We will continue to assume the wind is blowing from 12:00, only this time the bow is pointed at 4:00. You are on a run (or running before the wind) on a port tack. If you were to swing the bow through 6:00 (DDW or dead downwind) the main and jib would flop over with some force to the other side of the boat. If you continued to swing the bow around to be pointing at 8:00 you have now GYBED and are now on a run on a starboard tack.
3. Wear Ship:
This is another way to tack, where the goal is to get the bow from 2:00 to 10:00 as in example 1. Wind is still coming from 12:00. Assuming you are closed hauled with the bow pointing at 2:00 you are again close haled on a port tack. Your boat doesn't like to go through the wind so instead of turning the bow towards the wind, you turn it away from the wind. Your bow quickly swings through 3,4,5,6 (sails gybe here),& 7,8,9 o'clock and you end up at 10:00, close hauled on a starboard tack. You have just Worn Ship, and gybed around to your new tack.
4. Chicken Gybe:
This is a favorite way to avoid gybing in heavy winds where the force of the boom coming across the boat may do damage. Perhaps the wind is blowing hard (still from the 12:00 direction) and you are too short handed to have someone quickly sheet in, and quickly release the main-sheet for a regular gybe. As in example 2 you are on a port run with the bow facing 4:00. You want to get the bow to face 8:00 but you fear damage if you gybe. You turn the bow into the wind and the bow goes through 3, 2, 1, 12, 11, 10, 9 and you end up with the bow facing 8:00 on a starboard run. You have now completed a Chicken Gybe, as you tacked around through the wind to reach your new downwind course.
I hope that is helpful.