PAdding is a PArt of an element's PAinting: it extends the element's background. It makes sense to think of a pair element+padding as sharing a common background. Padding is analogous to the painting's canvas: the bigger the padding, the bigger the canvas and therefore background. Border (the painting's frame) would go around that pair. And margin will separate paintings on the gallery wall. Thinking about the concept of object background helps glue the pair object+padding together. The usual explanations of what is inside vs outside do not stick to memory: after a while everybody gets back to the original confusion. Remember also that margins are vertically collapsible and padding is not.
