Sorry for the confusion. Both statements are true, but to clarify:
Only one discount in each category can be applied to an order. The categories are:
Cart Item Total
Item Price (a specific line item in the cart, each item can have one such discount)
Shipping and Handling
If there is more than one discount applied to any of these categories, whether automatically or with a code, we will choose the highest discount possible. Between a $10 cart discount and a $20 cart discount the $20 discount will always take priority.
However, a $10 product discount and a $20 cart discount will both apply for a total of $30 off.
The last statement -- "Item discounts are applied before cart discounts -- i.e., item prices are marked down before a percentage would be taken off the Cart Item Total" -- means that item discounts are considered before cart (and shipping) discounts, so if an item discount lowers the cart total then a percentage taken from the cart total will be that much smaller. Also, if an item discount lowers the cart total below the minimum price threshold for a cart discount then that discount will not apply.
If you don't want different types of discounts to pile up then it is best to only use one category of discount. If you're looking to create a discount that can be used based on the overall quantity in the shopping cart then you should use a Cart Item Total discount with a minimum quantity setting rather than a series of product discounts.