The connection is that Mastodon is just one of the "applications" built on top of ActivityPub protocol. Others are Pixelfed, Pleroma, Peertube, Writefreely, and several more.

Being based on the same protocol, they are all to some extent interoperable - e.g. you can follow Pixelfed users from your Mastodon account.

"Fediverse" is the umbrella term for all of these applications working together. It is a portmanteau for "federated" and "universe". The "federal police" association is unfortunate, but it is something USA only - rest of the world doesn't really see this.