For a while they were pursuing re-usability through single-stage-to-orbit, i.e. a spaceship that can pretty much function as a plane but goes to space, without any staging. This turned out to be a dead end; the material science just isn't there to build a ship and a fuel tank that is both strong enough and light enough. And before that you had the Shuttle obviously, which ostensibly had re-usable parts but still cost like a billion per launch, because the external tank was ditched, the solid rocket booster were refurbished at a cost equal to building new ones and for the orbiter the main engines were pretty much taken apart and re-assembled before they were re-flown if I understand correctly.
In general SpaceX has been able to save cost because they do a lot in-house and don't have to deal with the pretty inefficient way the NASA manufacturing pipeline is set up. NASA has a ton of suppliers, facilities spread out across different states, which from what I understand is mostly a result of needing to secure funding and being spread out gives more political support from local representatives. But it introduces a lot of inefficiency. Like, a lot of the discussion around the Constellation program and later SLS re-using things from Shuttle wasn't because this is what engineers deemed best. It was because this would preserve jobs in the same places, which in turn preserves political support from the same people.