A Nephrologist is a kidney specialist. The Neph is taken from the nephrons in the kidney, of which there are millions.
A Urologist deals specifically with the urinary system, which includes the bladder and urethra and possibly the ureters as well. If men have prostate problems, then they would see a urologist.
Obviously, there is some overlap between the two, but if you are in renal failure you would be under the care of a Nephrologist and if you had just bladder problems, you would be under the care of a Nephrologist.