A clinical staff pharmacist is a typically a hospital staffer at either a specialty hospital or shares part time duties doing things a clinical pharmacist does. So they're mostly verifying orders, calling MDs, mixing chemo or verifying sterile compounding, supervising techs like a regular staffer/traditional hospital pharmacist most or all of the time.
Clinical pharmacists are the ones on the floors going on rounds, making recommendations, having more patient interaction. They're the ones with specialty certifications.