Matrix is the federated messaging network. It's also end to end encrypted, although people have pointed out issues with server security and with metadata—which is why they're working on peer to peer tech.
RCS is not similar to any federated technology at all. It's operated exclusively by Google in the US and most other countries. The technology was created, from the ground up, for carriers. But even carriers couldn't actually make it work in practice, so they asked Google to take over. It's a fucking albatross. We, as a society, need to drop it.