ThingSpeak Client to Connect Arduino to the Internet

Yes, you have the right idea ... there is a database component. It's a full web app with Charts, Apps, and Plugins that extend that base functionality - much like Wordpress is a PHP/MySQL front-end for blog posts with plugins. The goal is to make it easy and not have to run a local server if you don't want to or put this on a shared web host. An import tool is in progress so you can use the visualization tools if you have data already maybe from an SD card logger or something like that.

Sounds like you are making good progress with your project. Maybe they will link...