Final answer:
The process where functions managed by one set of brain cells are assumed by another set is known as brain plasticity or neuroplasticity, which is the brain's capacity to reorganize itself by forming new connections.
Step-by-step explanation:
The term for the process in which functions once governed by a set of cells in the brain are taken over by another set of cells is known as brain plasticity or neuroplasticity. Brain plasticity refers to the brain's ability to reorganize itself by forming new neural connections throughout life. This ability allows the neurons (nerve cells) in the brain to compensate for injury and disease and to adjust their activities in response to new situations or to changes in their environment. This is distinct from the differentiation process, which refers to how unspecialized cells become specialized cells like neurons or epithelial cells, but is related in the sense that both processes are crucial for maintaining and adjusting brain function.