Is there a difference between prostatitis and prostatorrhea?

Yes. Prostatorrhea is an abnormal discharge from the prostate which may be seen during prostatitis. Prostatitis simply means inflammation of the prostate gland.
See below . Prostatorrhea is the discharge of prostate fluid from the penis. Most often asymptomatic and a normal physiological discharge occurring in younger men who rarely ejaculate via either sexual intercourse or masturbation leading to prostate congestion and overflow of fluid.

Prostatitis is inflammation of the prostate and may be acute or chronic, bacterial or non-bacterial (most common). Symptomatic.