If you are using Woo-Commerce to manage your inventory and just want to receive the payment using your Clover POS, then you would need the Woo Commerce Clover Payment Gateway.
Once payment is made, you can also have it auto print the order to your Clover Device or you can manually print the order. You will also get emails.
If you want the Woo-Commerce inventory to sync with your Clover Inventory then you would need an additional app on the Clover App Market that offers the ability to sync your Clover and Woo Commerce inventory.
We recommend using Woo Commerce Clover Payment Gateway for retail and the "Smart Online Order WordPress" plugin for restaurants. We have some merchants using the Smart Online Order WordPress plugin for retail, however, it's not recommended as it doesn't print shipping labels and doesn't offer features that are retail-specific. Please keep in mind that it is not recommended to use Woo-Commerce Payment Gateway for Restaurants as this setup is not ideal for restaurants. This is because modifiers or add-ons and local delivery zones won't be recognized by Clover. Therefore, for restaurants, it is highly recommended to use our Plugin "Smart Online Order" and not the Woo-Commerce Payment Gateway.

https://wordpress.org/plugins/woo-clover-gateway-by-zaytech/
Remember both connect to the same Clover App called "Smart Online Order"
Tip: You can switch from the different WordPress plugins to see which one you like better
WooCommerce is an ideal solution for business owners who want to use their existing layout, inventory, and prices and then have their Clover POS process the credit card payments. Since Woo-Commerce offers many advantages over existing store interfaces, the Woo Commerce Clover Payment Gateway is a great solution to have the orders processed and printed to your Clover.
To get started, install this plugin.https://wordpress.org/plugins/woo-clover-gateway-by-zaytech/#description
then go to Woocomerce->Settings->payments choose Clover Integration and click on manage, put your API KEY, the gateway name (Will be shown on checkout page) and a small description, to get your API key, go to Clover.com then more tools and install our application ‘smart online order + WordPress’, after installing the app open it choose ‘I have WordPress website’ then chose ‘I want to install the plugin by myself’, copy the API key and past it in Woocommerce settings.