Discounts configured for All Cart Items take a percentage or flat amount off the order total or shipping amount, while discounts for a specific product only affect the base price of that item in the cart, so as you have seen, it is possible to have one discount marking down the price of an item while the entire order is also being discounted. A cart can have one discount applied to the whole order plus one discount applied to each item in the cart.
However, if you are having buyers enter a Discount Code to claim your discounts, you could create a discount for All Cart Items that takes 0.00 off the order total which uses the same Discount Code as your $4.00 off item discount, so when the buyer enters that code to claim the item-based discount, it zeroes-out the full-cart discount.