List the behavior the current type is actually doing
Payment methods: the Checkout block guide says Payment Options shows methods that are available in the store and compatible with the block, according to the gateway settings. The cart-and-checkout guide says an incompatible gateway may not appear on the block checkout, and if every enabled gateway is incompatible, that checkout can show that no payment method is available. Those sentences are about the block. They do not say what the classic shortcode will display. A gateway's own settings still apply on either type, and only that gateway's documentation can say the method appears after a switch.
The disappearing gateway is the symptom this order of checks is for. A method that was visible on the classic shortcode and is missing after a move to the Checkout block is, first, the compatibility rule above: confirm the migration actually happened on the assigned page, then read the gateway's own block-compatibility statement and its settings, then compare what each checkout type shows for the same cart. While you isolate the difference, leave the store's terms, shipping, coupons, and business description alone. A gateway missing from a new checkout type is a compatibility fact about that integration. It is not, by itself, the provider declining the business, and changing the business description is not a repair.
Buyer controls are not identical. Advanced settings say the classic shortcode shows terms inline, opened from a link, with a checkbox. The block shows a purchase sentence with links to the terms and privacy pages when those pages are set, and the block editor can change that sentence. The Checkout block also has its own terms checkbox setting, a coupon form that can be removed, and express-payment and local-pickup areas that appear only when their settings are on. The block local-pickup option is different from the older shipping-zone pickup the block guide calls legacy.
Custom checkout fields are a separate dependency. WooCommerce says extensions that add markup with hooks, including custom checkout fields, usually need integration work before they support the blocks. Order status, stock, and email still follow WooCommerce's order documentation after either checkout creates an order. Those systems are not converted by renaming the checkout block. Accessibility behavior is not compared here, because the pages above do not state a difference.