Each Cloudflare API allows you to achieve different goals.
The Partner API allows you to create a user account and add a domain (either CNAME or full DNS setups), which will be associated with your partner account and give you control to add/delete domains. The benefit of using the Partner API is that it allows you to use CNAME setup from the free plan upwards, while the Client API only has an option for full DNS integration. CNAME setup is otherwise only available starting from the Business plan and higher for direct customers.
The Client API gives you the ability to manage Cloudflare settings for individual accounts (e.g. update DNS records, select security levels, choose performance features, determine the caching level, create page rules etc.) for domains that were added via the Partner API.
The Reseller API, for those partners who have been qualified for the reseller program, allows you to create paid subscriptions for domains that are associated with a given partner account.
Please note, the Client API allows you also to add domains on Cloudflare but these will not be associated with your partner account.