In Bluesky you create an account on a specific PDS (personal data server) and need to authenticate yourself against that server to write content (posts, likes, follows, etc) to your user repository. Content in this user repository is signed and discoverable by relay servers, and app view services. Currently you can't move your user repository to another PDS, so your user is tied to that server for the time being. When posting content you post to the specific server your user repository is hosted in.

With Nostr your identity is truly decentralized. You create a user meaning a private and public key. You then choose which set of relay servers you want to post content to and which servers to pull content from. If you post content to servers A, B, and C users that pull from those servers see your posts. All posts are signed with your private key so the other users can verify that they were in fact posted by you. It does not matter which relay servers you post to, they will happily store your content unless they've specifically blocked you or require some form of white-listing.

So in that way your Nostr identity is not connected to any specific server, you can always choose to post to a different relay. As of today I don't think Nostr relays federate/distribute content to other relays, but this seems to be a possibility for the future.

Edit: Specified that Nostr relay servers don't have to be open by default.