The shuttle was a re-usable ship, the rockets used to get it into space were not reusable.
The Soviet lookalike did use a single use rocket as its second stage, with the reusable part just being an orbiter.
Sounds suspiciously like one of those projects you propose when you want something finer short term but assume that they never survive to the point where they actually need to deliver?
Refurbishment of the shuttle orbiter took months and tens of thousands of work hours before it could fly again. It was pretty far from what ordinary people understand under "reuse", though not completely outside the meaning of the word.
That said, refurbishing both the SRBs and the SSMEs after each use was labor-intensive and as such expensive.