Yes that's how it works. When you repost a note you're publishing it to all the relays that you write to. It extends the reach of the note.
Discussion
its a quite novel solution to content propagation, if we had a way to find npubs relays like a dht then we likely could find everything
I use nostr.watch to find relays.
I also run my own uncensored relay.
yep but clients should be automatically finding relays for npubs not on the same relays
manually managing relays struck me as one of the least user-friendly aspects of setting up my clients. they came with defaults, yes, but different ones, so i'd have different views of Nostr depending on which one i was using, until i "synced" them all using the shared list that's stored in the profile metadata.
also writing to 10 to 20 relays is not efficient