The reason why any cell of the body is different from a neuron (brain cell) is because they all have quite different functions.

The cells in the body have a specific function according to the organ that they conform: liver and kidney cells, heart cells, skin cells, etc. Brain cells or neurons have to interact with each other in order to stimulate other brain cells, so they secrete a chemical called neurotransmitter, which triggers action in other neurons. Brain cells or neurons are responsible of the body function, and they have to control body movement, consciousness, our senses, etc. Neurons act in a more global sense than any other cells in other organs of the body.