Look, I have a degree in economics and it took me awhile to wrap my massive head around the difference between demand and quantity demanded. Now that I know the difference, I see the two being misused all the time. So, once and for all, here is the difference between demand and quantity demanded.
Demand refers to the amount of a good or service that consumers are both willing and able to buy at given prices during a period of time.
Quantity demanded is the amount of a good or service people will buy at a particular price at a particular time.
The big difference, the quantity demanded refers to a specific price point whereas demand refers to the amount people are willing and able to buy plotted out over all price points.
Demand is plotted on a graph as a line and quantity demanded is plotted on a graph as a single point.
When we say that there has been a change in demand for a product or service, we mean that the whole demand curve has shifted inwards or outwards and that the units demanded at each price has increased or decreased simultaneously.
When we say that the quantity demanded has changed, we mean that due to a change in the price of the product or service the number of units that consumers are willing to buy at the new price has changed.
For example, raising the price of a product from $7 to $10 will change the quantity demanded but will not reflect a change in demand.