Final answer:
The neural plate develops directly into the neural tube, which will differentiate into the brain and spinal cord, while neural crest cells adjacent to it will form peripheral nervous system structures and other tissues.
Step-by-step explanation:
The neural plate develops directly into the neural tube, which occurs during a process known as neurulation. This follows after the process of gastrulation in early embryonic development. Within a few days, the thickened layer of neuroepithelium that forms the neural plate begins to change shape, buckle, and fold inward, and its borders converge to form the hollow structural neural tube underneath the ectoderm. The anterior part of this neural tube will differentiate into the brain while the posterior part will become the spinal cord. The neural crest cells, which develop alongside the neural tube, will go on to form structures of the peripheral nervous system, as well as other tissue types such as craniofacial cartilage and bone, and melanocytes.