"Demand" is often used in economics. It refers to how much people want something or, more specifically, whether they're willing to buy something and how much they're willing to pay for it. There can be a demand for things that people need but there can also be a demand for things that people merely want. "Need" refers to how much people need something, regardless of whether they know they need it and regardless of whether they want it.

We have a need for food. We have a need for oxygen. We have a demand for STEM-educated professionals, for oil commodities, for sitcoms...

Short, short version: Need is need. Demand is desire.