The choice between Block Checkout and Classic Checkout in WooCommerce primarily depends on the version of WooCommerce you are using.
As of WooCommerce version 8.3 and later, Block Checkout is the default experience. The Classic Checkout, which is based on shortcodes, is still available but requires manual activation, depending on your WooCommerce settings and theme compatibility.
WoodMart is a premium WooCommerce theme that generally supports both Classic and Block-based checkouts. However, please note that certain features or customizations may behave differently depending on which checkout method you choose.
Additionally, as we mentioned, if your checkout page is created using shortcode, you need to add and update the fields in the Checkout Fields section. Conversely, if your checkout is configured using WooCommerce Blocks, the fields need to be added and updated in the Blocks Checkout Fields section.
Please refer to the below links for more details.
https://woocommerce.com/document/woocommerce-store-editing/customizing-cart-and-checkout/
https://tonjoo.com/revert-woocommerce-checkout-page-to-classic-editor/
Hope this helps.
Thank you!