Customers see your online store (theme) first, then checkout when they pay. Smarty applies discount math at checkout. Some Smarty features also need your theme to show messages or widgets correctly.
Checkout (where the price is final)
If something looks wrong, fix rules and dates in the discount first — not the theme.
Online store (theme)
If the storefront message looks different from the final checkout amount, trust checkout first, then review FAQ and your discount setup in Create a discount.