Spinal cord. Actually yes, it is also called medulla spinalis, medulla means a structure in the middle of the organ and spinalis is related to the vertebral spines as the peripheral nerves originate from the spinal cord on both sides of the vertebral spines.
Medulla. In old anatomy, medulla spinalis refers to the spinal cord and medulla oblongata refers to the back part of the brain (that is now commonly referred to as just medulla). Different parts of the spinal cord have separate names, such as conus (bottom portion).