Not exactly. The way WooCommerce gateways work for example is they pass the customer, the card, and then store the tokens against user meta. Last 4 digits and perhaps card type.
Then on checkout, it will show Visa ending 1234 and they can select it. Instead of passing card info, it passes token of card to charge.
So rather than only pass the info, it has a save and a render function basically which makes it a lot easier to checkout multiple times.
If you went to say Stripe.com and deleted the customers cards, your website will still show the card info which would subsequently fail if they tried to use it, as it has no real integration with the provider. It’s a pretty simple feature yet very useful for multiple-use style cases.