urology; urology department
Refers to the medical specialty or the hospital department dealing with urinary tract and male reproductive organs.
My father had a prostate exam at the urology department.
Urology deals with diseases of the kidneys and bladder.
泌尿器 refers to the actual organs (kidneys, bladder, etc.), while 泌尿器科 is the medical department/specialty (urology) that treats them.
urologist
Compound of 泌尿器 (urinary organs) + 科 (department, field of study).