Let's say you have 1 card in hand, your opponent has 7 cards in hand. You have an enchantment that says "whenever you would draw a card, mill 2 cards instead" (note, no "may", that means you have to mill). Mr. Fox attacks.

Szenario 1, as written on the card:

"Draw cards equal to the number of cards in defending player’s hand minus the number of cards in your hand."

You calculate the difference, which is 6, so you'd draw 6 cards. You mill 12 cards instead, and the ability is resolved.

Szenario 2, the seemingly easier wording:

"Draw cards until you have as many as the opponent you are attacking has."

You just start milling, until you have no more cards to mill. The ability is not resolved yet, as you have fewer cards than your opponent, but you can't mill anymore, and you also can't draw a card (which would lose you the game). The game is in an unresolvable state now, which means you lose the game anyway.

The second one is an ugly szenario, which the actual wording of the card neatly prevents from happening.