In short: Product and order discounts are labeled with your discount code, or the title for automatic discounts. Shipping discounts are labeled FREE SHIPPING, X% OFF SHIPPING or X OFF SHIPPING.
Labels
Product discounts: the code or title appears next to each discounted item, with the saving.
Order discounts: the code or title appears once, on the order subtotal.
Shipping discounts: the shipping line shows FREE SHIPPING, or for example 50% OFF SHIPPING or 5 OFF SHIPPING.
When they appear
Automatic discounts apply as soon as the cart qualifies.
Discount codes apply once the customer enters the code in the cart or at checkout.
Shipping discounts appear once checkout shows shipping rates.
Product and order discounts with a Shipping Country condition use the country selected in your store, so they can appear in the cart. Shipping discounts wait for the shipping address.
Good to know
Whether discounts show on the cart page depends on your theme. Checkout always shows them.
The code or title is shown exactly as you typed it, so you can write automatic discount titles in your customers' language. Shipping labels are always in English.
If the cart changes and stops meeting a condition, the discount is removed straight away. It comes back if the cart qualifies again.
OneCode: Stackable Discounts doesn't add banners or progress bars to your store. To tell customers about tiers, mention them in your product pages, announcement bar or emails.