Is WooCommerce a WordPress plugin?

They have the same company behind WordPress, Automattic, which bought WooCommerce and WooThemes in 2015. WooCommerce is a WordPress plugin - so no you cannot use WooCommerce without WordPress.

Yes, WooCommerce is a free open-source e-commerce plugin for WordPress. Its currently owned by the creators of WordPress also. By adding a WoCommerce plugin to WordPress you'll transform your website into a powerful e-commerce store and sell products.

WordPress is an open-source Content Management System. You can use it to create and maintain online websites and blogs. Woocommerce profit plugin can be integrated into WordPress to change it into an eCommerce store.

Although if you only need to use Woocommerce, you can use it without having an account on WordPress. The Woocommerce community mostly uses the software independently or integrates it with any other software like Shopify, WordPress, Amazon, etc.