Herniated disc, pinched nerve and bulging disc get used as if they were one thing. Here is how the three terms relate, and where a clinician has to take over.
How the three terms connect
The Cleveland Clinic says that over time, stress and repeated movements can cause the disks in your spine to weaken, causing a herniated disk or pinched nerve. Both terms are named as results of the same weakening, so treat them as related and not as rivals.
What happens inside the disk
OrthoInfo (AAOS) describes a disk with a jelly-like center. If the pressure continues, that center may push all the way through the disk's outer ring, called a rupture, or cause the ring to bulge, called a slip. Which of these is worse for a given person is a question for the clinician reading your imaging.

Getting a name for your own case
Names matter less than the exam that produces them. Read general background first, such as the WebMD pain management center, the OrthoInfo sciatica page and the American Academy of Pain Medicine. Then ask a clinician in Little Falls or nearby which term fits your imaging and symptoms. Also ask what the proposed plan involves over time.
Who names your diagnosis
Telling these conditions apart is work for a clinician's exam. Our comparisons stop short of medical advice, and a clinician decides your diagnosis.