Holding down shift and left clicking items in inventory windows will switch them to another inventory window...most of the time.
Open your character's inventory, then open a chest, and without moving open your equipment window. All three windows should be open at once.
Shift click a hat in one of the inventories (with no hat on) - It gets equipped
Shift click a hat in one of the inventories (with a hat on) - nothing happens
Shift click a bucket in one of the inventories (or something else that cannot be equipped) - nothing happens
These are inconsistencies and therefore bugs. If I learn that shift click moves something from one inventory to another, shift click should ALWAYS do that. There are multiple acceptable fixes for this though. A message saying "This item cannot be equipped." when shift clicking a bucket is probably the easiest. Even though the player probably meant to move it to the other inventory window it is now understood that with the equipment window open shift click is trying to equip it and not move it. Thats still silly but it might fix the 'expect something - get nothing'.
An alternate more preferable fix is to make it so that A> Items that can be equipped but already have something in their slot get swapped out. However, this would also have to be implemented when equipping things the general way (left click to pick it up, left click in equip menu to equip it). B> Buckets and other unequippable objects should always assume shift click means switch inventories and not 'try to equip'.