A federated system is in a decentralized system too, but I reckon you're asking about the difference between something that is decentralized in the way Bitcoin or similar systems are, versus the federated software of the Fediverse.
This might be an oversimplification, but the main difference comes mostly down to a philosophy on state and statemanagement.
A decentralized system in the style of Bitcoin and such are a single source of truth decided by consensus of many independent actors(servers) where none of them have any more influence than the other.
However it is important that all actors agree on the entire state of the system, you can't have an actor that only cares about transcations of exactly 420$ for example.
If some servers have a different view which transactions are true; this is a problem for bitcoin as the system requires a single consensus of whats real to work. (I'm no BC expert, but this should be true on a high level, even if there are practical solutions to this)
On the other hand, a federated systems like on Mastodon are a bunch of independent servers which have their own state(ie posts and what not). They are the ultimate owner of said content, in the sense that that they don't need approval of any other member in the fediverse to post that content. The decentralized part of the fediverse is obviously the fact that fediverse servers shares its posts with all other servers it knows off, but its not expected behavior that all servers in the fediverse has to have all posts, and the system is not degraded should some posts be missing.
This doesn't seem entirely accurate to me.
Most public platforms interacting with the Fediverse today does require you to register an email address out of practical considerations but this is not a requirement of the system in itself. It is possible to both post and read an unmoderated fediverse with enough effort.
If you don't like the moderation of your particular server, you are fully able to create your own or set up an existing solution yourself that gives you 100% control over what kind of content you post, and in turn which content you federate to your server. Of course, you can't control which servers decide to allow your content on their server, but any user of servers where your content is blocked can do the same and have access to your content again.
As far as privacy goes, you can rent servers and purchase domains with crypto currencies which are not traceable back to you where you can host your own service that interacts with the fediverse, making you 100% able to control the information you post into it.