No, these two terms describe different processes.
DDD stands for degenerative disc disease. When discs age they loose water and become dried out and brittle, like a rubber band that you leave out in the sun. Once it is dried out if you pull on it it won't stretch but it will break instead. So, degenerative disc disease is basically like arthritis of the disc.
A bulging disc is a slight protrusion of the center of the disc (nucleus pulposus) into the spinal canal. Bulging discs are very common, and may not produce any symptoms at all as the annulus fibrosus (outer ring of the disc) has not been ruptured. If this outer ring ruptures, it is then called a "herniated disc".
Perhaps it's not the discs themselves that are painful, but maybe they are applying pressure to the nerves that travel to your leg and foot. Wait for the neurology report to come back, and let us know what is reads.