What is the difference between the concepts of demand, demand schedule and quantity demanded?
Can these be used interchangeably, and do any of them have multiple meanings in economics?
Also, is there a difference between shift in demand and increase in demand?
To see how these concepts are frequently confusing students, see the questions
What is the difference between the demand schedule and the demand curve?
There is a difference between the 3 concepts. They should not be used interchangeably in rigorous explanations and textbooks such as Mankiw's Principles of Economics do not use these words interchangeably.
Demand
Demand typically refers to the whole demand relationship between price and quantity demanded. If you are asked to plot supply & demand or just demand you are asked to produce graph of demand function.
So a demand can be given by:
$$Q_d= 100-P \tag{1} $$
and the above would be demand. More graduate sources will typically also say 'demand function' but even in graduate textbooks such as Varian Microeconomic Analysis 3rd ed ch 9 will refer commonly to demand functions as just demand.
Quantity Demanded
This is some specific quantity demanded. It is a point along the demand function but not the whole function.
For example, continuing to use eq. 1 if price is 10 quantity demanded would be 90.
So the quantity demanded is some specific value for a function. It does not need to be explicit number. For example, $Q^*$ can be the equilibrium quantity demanded. The point is that quantity demanded will be some particular point given by the demand curve at some particular price.
Demand Schedule
Demand schedule is a particular way how to capture whole demand. It is analogue to demand 'graph'.
Below you can see an example of demand schedule from Mankiw's Principles pp 120. As you can see demand schedule is a way how to also capture demand function by putting it in a table or in another words schedule.
Also, is there a difference between shift in demand and increase in demand?
No as far as I can see or if there is any difference even textbooks mistakenly use them interchangeably. For example, on pp 305 Mankiw refers to graph that shows shift of demand function as an increase in demand.
However, one needs to be very careful here because increase in quantity demanded would be just change along demand curve (that is just change in quantity demanded as a response to price change) not shift of the demand curve (which means quantity demanded changes at every possible price), but I think I seen sources that are not so careful with terminology.
Where the Confusion Probably Comes From
Some of the confusion might stem from loose use of this terminology outside profession.
In media people sometimes use word demand as a shorthand for quantity demanded.
This usage is however incorrect, in economics it is clearly important to distinguish between demand and quantity demanded especially the distinction is important in supply demand analysis.
PS: I teach econ 101 to undergraduates and I can concur that students often make mistakes between quantity demanded and demand.
However, I did not have many students who would be confused about demand schedule.
