There is actually a quality difference between the compression levels, but it's not always easily seen with standard photos. If the photo had areas of all one color, such as a large white board, or blue sky, the compression would be more visible. The compression works by taking some of the pixels, and making them span several nearby pixels that are almost the same color. (Simple explanation)
Your computer monitor has a resolution of 72 dpi (dots per inch) whereas a printer can range from 300 to 2400 dpi. When you print the picture, the "spanned" pixels are spanned again several times more, make larger areas of a single color, therefore making printed images a lower quality do to large "blocky" areas of a single color (or almost single color).
See the area in the attached picture: