Yes, but you can add a couple of points to that. Rocket Lab is more aggressive than SpaceX about designing a system which is cheap and fast to turn around for the next launch. They got fewer and simpler engines to inspect and fix. Keep in mind they SpaceX today spends around 2 months to prepare a recovered booster for launch. Rocket Lab is aiming to do the same with 24 hours with Neutron.

This will affect costs a lot because it means you need a smaller inventory of rockets to keep the same frequency of launches.

Hard to tell how quickly SpaceX will manage to prepare Starship for launch. It will be engines which need no cleaning but they are more complex than current engines and there are more of them.