Adding because Nostr seems to be marketed as something more decentralized than that, and I'd like to get a deeper understanding.
With mastodon your client only talks to one "instance" to see all the "instances" that "instance" is federated with.
With Nostr your client connects to every "relay" you want to see content from, there isn't really any communication between "relays".
assuming it's the same as Scuttlebutt (also gossip protocol) a relay is literally just a relay. There's no "home server". You don't have an account on anyone's machine. You just shove data out to "people" who are listening to you. In scuttlebutt the relays are configured so that anyone can ask it to "follow" them and then they send their data to it. Anyone who listens to that relay can get any data the relay has.
in scuttlebutt the problem was that I never felt like i could trust a relay to exist for more than 6 months, so i just followed every one i could. No-one wants to set up a relay, and relays have to have a static domain / ip so that you know where to look for them. It's not like tor where you can just leave your computer on and that's good enough. I expect the same problems here.
This makes it way easier for people to write clients or bots or whatever, but it also tosses out many of the guarantees people who used the original scuttlebot took for granted.
When you follow someone, or someone follows you, the follower's client will get a list of relays the person they want to follow is posting to. The follower can connect to any of those relays and get any new content.
On many relays it's possible to get a firehose feed of everything posted to that relay. On free public relays this firehose feed may contain lots of spam accounts.
The protocol is surprisingly simple to read [1], many relays and clients exist already.
I exchanged messages with a friend of mine who was using a very different client and it just worked!
Personally I like the fact that you can 'like' posts by sending a couple of sats via Lightning. I think it is a great motivator to write thoughtful, quality content.
Currently nostr is radical, weird and unpolished. The Amethyst client is slow at times. But the pace of development is incredible.
[1] https://github.com/nostr-protocol/nips/blob/master/01.md