Yes, both systems are reusable, but there are key differences in the refurbishment of the systems that partly explains the cost difference. It took more labor, resources and time to refurbish the shuttle. Also consider rapid reusability was a stretch goal when it was being designed, but we have come a loooong way since, spacex in particular has had it as a driving competitive differentiator for years now.
Another big difference is that NASA post Cold War was a skilled jobs program, with an incentive to do distributed, high overhead work to appease their bosses (congress), while SpaceX has the opposite.