Another way of understanding demand and consumption is with a "filling the bucket" analogy. Suppose you want to fill a 5 gallon bucket with water. You can use an inexpensive hose connection to your sink providing 1 gallon per minute to do it, and it will take 5 minutes. Or you can get to a more expensive large faucet that provides 5 gallons per minute, it will fill in just one minute. The flow rate is the equivalent to demand, and the 5 gallons of water are equivalent to consumption. In this example, filling both buckets has the same "consumption" but very different "demands."
The same is true of electricity. While you may be able to accomplish the same thing by operating a small wattage appliance for many hours as operating something of higher wattage for just a few, the higher wattage piece of equipment will create a higher demand on the utility. Using our analogy, you are asking for a larger pipe, and that costs more. If time is of the essence, it might be worth having the more expensive high flow rate or wattage. This is why utilities often charge some customers for both demand and consumption. A customer that sets a high demand requires more services from the utility--additional generating plant capacity, and more expense in lines, transformers and substation equipment.
Some people like to use a car analogy to explain and understand how demand and consumption relate. The car's speedometer is like the demand meter and the odometer is like a consumption meter. Two cars could travel the same 100 mile road, one at 10 miles per hour for 10 hours and the other at 100 miles per hour for 1 hour. It takes a much more capable and expensive engine to power the car at 100 miles per hour than it does to power the one going only 10 miles per hour.