Two e-commerce in two different folders of the same domain

I would like to know if you have to install wordpress also in the subfolder, so a wordpress installation for each woocommerce plug or can you manage the two online shops even with a single installation?

Both options work, either 2 installations of WordPress with WooCommerce installed, or a single installation of WordPress set up as a multisite.

Neither will give a performance benefit over the other, but the multisite install will be simpler to maintain