Does a Shopify mobile app use Shopify checkout?

A properly built one does. TicApp apps hand off to Shopify's own checkout, so your payment methods, taxes, discounts and order records carry on working exactly as they do now. Nothing about how you take money changes.

This matters more than it sounds. Checkout is the most regulated, most tested part of an ecommerce stack, and rebuilding it is how apps end up with payment methods that half work.

It also means your Shopify admin stays the single place orders live. There is no second system to reconcile.