The core WooCommerce plugin by default doesn't have a payment processing capability built in - meaning it has no way to capture or process credit card information without the assistance of a third party plugin or payment processor. WooCommerce Payments however is a service that's offered in ADDITION to the core WooCommerce plugin - in this instance, the WooCommerce Payments gateway acts as the payment provider - but once again, the core WooCommerce Plugin and the WordPress CMS don't store or process credit card information.