An Increase in Demand vs An Increase in Quantity Demanded
Precision in Using Words or Economics as a Second Language
An Increase in the Quantity Demanded
The Quantity Demanded is an amount at a given price while Demand is the entire relationship between the various Quantities Demanded at a variety of prices.
When the price decreases from P1 to P2, the quantity demanded increases from Q1 to Q2.
Changing the price leads to changes in the quantity demanded.
Putting an item on sale will increase the quantity demanded.
An Increase in Demand
Demand is the relationship between Prices and Quantities Demanded.
Changes in things other than the price of the good or service may lead to changes the demand.
After the "jam band" Phish performed their last gig, the sales of soap and shampoo increased. (paraphrased from a late night comedian)
So to an economist, demand is not the same as the quantity demanded.
Just as Lindt Chocolates are not the same as Chocolate Lint.