The difference between quartz and agate, (your quartz rock is the same chemically as agate, chert, flint, chalcedony...), is one is microcrystalline and the other macrocrystalline. Quartz has some cracks. Its crystals are large enough when you run your thumbnail over them, you can feel the grains. The quartz is macrocrystallinear. All the others I mentioned will appear shiny and smoother than all the other beach rocks, not have any cracks and where the rock is chipped you will see concave divots. They are known as conchoidal fractures. The same fractures flint knapping hominids used to form their handtools.
The others are smooth, even waxy, to the touch. The crystals are microscopic. If you run your fingernail across the rock it will not catch. These rocks are all very hard. You will not be able to scratch them with a common nail. I assume you wer looking for agates. If you want to know more, the Agate Lady, Karen Brzyz, wrote a book. I think it is one of the best. I am not sure the name is the right spelling. But she will be the person that comes up.
Whitefish is the most picked over beach. Vermillion Beach has more solitude, less traffic. Wildcat Beach, too. Just saying. My favorite is Crisp Point Beach at the Crisp Point lighthouse. Do yourself a favor. All those flashy pictures are cut and sanded specimens. Google rough lake superior agates and hit images. Those will show you what you are looking for.