The quantity supplied means that this is the number of businesses that are currently in a positive state that are providing certain goods for a specific price. When you say quantity supplied, you are looking for an actual number. This means that when referring to the entire curve, the quantity supplied can be used.
The supply curve is the line that you will see on the graph that would refer to the various quantities that are used. This would refer to the different amounts that will be used for certain goods. It is possible that some goods are priced differently depending on where they are being sold. The supply curve can easily show that.