Are BPH and prostatitis the same thing?

No. BPH means benign prostatic hyperplasia. This is the enlargement of the prostate that most men experience with age. Prostatitis is inflammation or infection of the prostate gland.
No. They are different conditions that are completely unrelated. BPH is a genetic tendency for the prostate large as one ages and is not an acquired disease. Prostatitis is an acquired infection or inflammation of the prostate. The treatments for the two are completely different.