Hope this doesn't come accross as rhetorical, it's a genuine question!

Nostr users, how does this differ in your experience from Mastodon? At first glance it seems like the same idea but with the extra ingredient of blockchain, I'm not sure what this adds though, anonymity?

First of all there is some confusion because blockchain doesn't play a role here.

You start by creating a pair of public/private keys. That is your "account" but is independent from everything else (e.g. not tied to any specific tool nor web service).

Then you create texts (notes) which are digitally signed with your private key. Using the public key anyone can verify it was you writing it and nobody else.

There is no blockchain in the process, these simple text messages get sent to a multiple number of relays (you can even host them yourself) and other people can read them very freely.

The main difference to mastodon is that exists no central server where someone registers an account and has the power to kick you out from the site (deplatform). This also solves the problem with the mastodon servers decides to stop the service and suddenly everything is gone.

On NOSTR your texts are your texts, and there are multiple copies everywhere (more than 1000 free relays at the momment).

The fundamental difference is that with Mastodon, or any Fediverse service, the server still has full control over the user. It's basically no different from regular Facebook or Twitter, just with some optional federation on top that can be switched off at any time (and often is).

On Nostr the server is just a dumb relay, it controls and owns nothing. User identities are proper public key pairs. If a relay goes evil, you can just use another one or use multiple at once to begin with, since the location of the messages is irrelevant, everything is held together by public keys.

Last time I checked(years ago), it was like Mastodon but there are only dozen servers, and posting once in standard clients post it on all servers. Everything is a tweet, and servers serve you contents based on what it remembers about you. The core principle is that bans and refusals by server operators are at best customary since users can receive the same information elsewhere, even transparently.

Though, they did happily filter Macau casino spams flooding the system, so I wouldn't be so sure. Workload of posting to and receiving from dozen servers was also not trivial when I was trying it out, and architecture changes to reduce duplicates and/or syncing databases across hosts were actively discussed. I guess those works were never completed judging by comments here?

From my observation the federation is largely split between sides that don't like each other. The main block where the main instance lies is very trigger happy to block entire instances and if a server administrator doesn't follow the group think other server administrators will block you out of "lack of moderation". Account portability exists but requires that you be in good terms with the server admins. Which is fine. Their database and they do what they want but it felt like Reddit with less professional moderators.

On Nostr your account is your signature so there is no such thing as creating an account on someone else's database. You push to multiple relays where people can follow you so even if relay operators ban you there will always be some relay willing to host your stuff.

Others already pointed out there is no blockchain involved other than using the same secp256k1 as Bitcoin for signatures.

There is no blockchain, only basic cryptographic signatures on each message. And users are not tied to any servers, they can read from multiple or write to multiple. They can (locally) aggregate data from many servers or connect to a specific server, same for publishing, it's very flexible and different clients choose to do it in different ways and expose different interfaces to users.

I was on mastodon, but the instance that was hosting my account got shut down, so I don't have my account anymore. That can't happen on Nostr. You need to make sure that you store your "private key" (sort of like password) safe.