Everything is interoperable, but there also is no truly global state. Primal attempts to replicate one, by pulling in the vast majority of notes from other relays into their massive caching relay, but even that doesn't have absolutely everything.

Therefore, on most Nostr microblogging apps, you will see the notes that are stored on the relays you have set up to read from, and you may see some notes from those you follow that are stored on other relays, IF your client is using the outbox model to fetch their notes from the relays they write to, regardless of what relays you have set up. Meanwhile, Primal will be able to display almost any note that fits in your feed criteria, unless it is only being stored on an obscure relay that Primal doesn't pull notes from.