@ikea_femme continuing the email metaphor: It's like the difference between Gmail and Yahoo Mail.
You can have an account on one and still send messages to the other. This is the federation part.
Both come bundled with their own user interface, but you can also interact using a third party client, like mail.app on iPhone, or Outlook.
As for the backend details, I don't know. Light vs. Heavyweight is more of a design philosophy and can manifest in several ways.
Hope that helps!