HATS to POOP.

The first move matters.

HATS has 19 valid one-letter neighbors in this dictionary. 3 of them can begin a shortest path:

Each of these leaves 4 moves to POOP. The other 16 neighbors are valid moves too, but cannot reach the target in the minimum from this starting word.

Follow the changes

The highlighted letter beside each step shows exactly which position changed. This historical solution uses the original puzzle’s dictionary and minimum move count. Other shortest routes can take different intermediate words.