Difference between Cloudflare CDN and NGINX
Cloudflare does not serve static content itself. It only caches content originally served by some other server. You still need that other server -- known as your "origin server". You might still use nginx as your origin server. By putting Cloudflare in front of it, you can make your site faster and more secure, but Cloudflare does not replace your server.
From, How does Cloudflare work?:
The Short Answer, Cloudflare protects and accelerates any website online. Once your website is a part of the Cloudflare community, its web traffic is routed through our intelligent global network.
In terms of differences, you can't directly compare Nginx with a CDN (a group of services including Nginx), you can create a CDN using Nginx.