This guide details the steps to help you to change your plan on Cloudflare using the Cloudflare API. You can always change your plan within the user interface of the Cloudflare portal, however, you may be looking to change your plans in bulk and that is where using the Cloudflare API makes more sense.
For the purposes of Cloudflare settings, a "zone" or "domain zone" is Cloudflare's naming convention for a "website" URL address.