Change in quantity supplied occurs when only the price changes.Here the other factors are assumed to be constant. Take the example of the bicycle in the material ( I don't have it with me right now, so please refer the 2nd chapter). If there is a price change, you can see that the quantity also changes. Higher the price, more will be the quantity supplied But these changes are along the supply curve itself.Therefore these are "movements along the supply curve." In other words this is the "law of supply."
Change in supply curve occurs when everything other than price(such as income, fashion, taste,govt policies,etc) changes. For example if the government subsidized the production of bicycles or if the cost of the parts of the bicycle were to come down, the curve will shift to the right now they will be able to produce more at a lower price( conversely if it was taxed it would shift to the left).Therefore these are called "shifts in the supply curve."
The answer to your second question lies in the definition of these terms.
Hope this helped.
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