If you leave a sailing yacht (no sails set, motor off, rudder centered) all to itself it will eventually align with the direction of the wind. The stern will point to where the wind is coming from and the bow will point to where the wind is going to.

If the boat is anchored (at the bow) it's the other way round: the bow will point into the wind and the stern will be where the wind is going.

(I hope my observations are right - otherwise all of this won't make any sense)

Each of these scenarios individually observed is clear to me in a "what else should the boat do?" kind of way. But the exact physical explanation would be interesting.

Particularly the first case is the one I'm struggling with: is the bow moving away from the wind because it is lighter than the stern? Or is it because of the shape of the boat? Other reason?