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Many people use these terms interchangeably but they are actually different. Let's see how these terms can be differentiated in very simple terms for clear understanding.

Fuel economy

Fuel economy is simply a term that describes how far a car can go with a particular quantity of fuel. A popular unit unit used for fuel economy is MPG (miles per gallon).

MPG is what is used in EPA rating to rate how fuel economical a car is.

Fuel consumption

Fuel consumption stands for the amount of fuel consumed per certain distance covered. For instance, a liter of fuel per hundred kilometres.

Fuel economy and fuel consumption are often used interchangeably but they have inverse relationship.
A car with low fuel consumption is more fuel economical while a car with high fuel consumption is less economical.

Fuel efficiency

This term is often wrongly used to mean fuel economy but it means a different thing. It is how efficient a car's engine burns fuel and it even goes beyond that when we consider factors like the car's aerodynamics, transmission design, tires and other factors that makes the car to do more work from a quantity of fuel.

In order to understand clearly the difference, let's use German brands like BMW or Mercedes benz compared with Asian Toyota as example. 
The German cars are more fuel efficient because there are advanced technologies built in to make them more fuel efficient but the Toyotas even while being less fuel efficiencient are more fuel economical and consume less fuel in certain drive conditions.

How fuel economical a car is has a direct relationship with the fuel efficiency and some other factors like the overall weight of the car. Therefore, a car that is fuel efficient and light will give the best fuel economy.