Good points, they are more similar than I had perceived. The fundamental objective in Bitcoin is the decentralized construction of an immutable ledger (through consensus attained by proof-of-work). It basically is a persistence layer. Whereas the fundamental objective in Nostr is to prevent central censoring of messages, so it's more akin to a communication protocol. However, censorship resistance is also a property of Bitcoin.
In what ways is the architecture similar? As far as I can tell, the only similarity to Bitcoin is that it is a "permissionless" protocol. Any relay can participate in Nostr, just like any node can participate in Bitcoin.