Hello and thank you for coming to Just Answer. We appreciate the opportunity to help you with your questions. I can't tell what level of understanding you currently have, so if my explanation is too basic, let me know and I will keep working with you until I can find the right level of information to answer your question to your satisfaction.
The demand curve is the measure of the amount of something consumers will purchase at a given price. With all other factors except price held constant, there is movement along the demand curve. When a merchant lowers the price of a good, the public will buy more of the good from that merchant. A shift in the demand curve occurs when other factors besides price change the situation. A shift in the demand curve is the result of something that makes the consumer see the good as more or less desirable regardless of the price. The new factor moves the demand curve up or down, resulting in more or less quantity of the good purchased at the same price as before.
One example you could use is ice cream. If you chart the demand curve for ice cream, then as the ice cream store increases the price of ice cream, people buy less ice cream. If the store reduces the price, people buy more. But if a heat wave strikes the area and outside temperatures soar, people will buy more ice cream regardless of the price. The hotter day causes a shift in the demand curve. Consumers will buy more ice cream at every price than they did on a cooler day.
This is a simple example of an elastic demand curve. If the price drops, people buy more and if the price rises, people buy less. The amount people will buy at a given price can change based on other factors that cause a shift in the demand curve, so that people buy more or less of the good at the same price than they did in the absence of the new factor.
There are other types of goods with demand driven by other factors that have to be modeled by other types of demand curves. Not all goods can be modeled by a simple elastic demand curve of price versus quantity. For example, gasoline is controlled by a mostly inelastic demand curve. Over the short term, people still have to buy about the same amount of gas regardless of the price. They can't just buy a lot less when the price rises because they still have to get to work and other places. There is some reduction of use, but the majority of uses aren't optional. Over the long term, people will buy new cars with higher gas mileage or move to different places closer to their jobs or make other changes but these changes take time. There are also demand curves with an upper quantity cap. Some goods people will only buy so much of, regardless of price. Milk might be a good example. You can only use so much milk before it goes bad, so even if the store is giving milk away, you will only demand a certain quantity before you don't want any more.
If you need more information about the types of demand curves, please let me know and I can go into detail about it. I hope the example of the ice cream and the explanation answer your question about the different between moving along the demand curve and a shift in the demand curve. Please let me know if you need more help with the difference. I can probably find other examples in my textbooks about external factors that can cause shifts in the demand curve, if you need more information.