I’m a Geologist, but my emphasis is sedimentology and stratigraphy, not petrography and mineralogy. Plus I research rocks of the western US now, which are in general much younger than the Michigan area – but I grew up in MI, so I will do my best, and there are few things I can say that might help. Like most questions asked of Geologists you are going to get a far more boring and wordy response than you signed up for...
First off, the color red, red = oxidized iron almost 100% of the time - just think about rust on old cars. You take iron and oxygen and your get shades of dark red rust, add water which acts as a weak acid, and you speed up the process, add salt and it goes even faster. So parts of the red/brown clasts contain iron bearing minerals. When I look at this I see 2 different major compositions. 1) The angular (very angular) dark red to brown clasts, probably shale to slate or mudstone, to maybe sandstone if the grains are large enough and 2) Off-white to light yellow matrix. The white matrix looks to be quartz which is a common form of silica – common in almost every rock. The other option is calcite, but calcite weathers and is usually softer, so soft that large rocks with a pure calcite matrix are far less common than quartz. Without scratching the rock, or the ability to drop dilute amounts or hydrochloric acid on it, I cannot tell if its quartz or calcite, but quarts seems the most reasonable. The most interesting part of this rock are the dark red angular clasts. The rock itself is rounded, probably been tumbling around in the lake (or river) for longer than most people can conceive and transported some distance from where it was found, but the inside is not rounded. This tells me it formed and was cemented into a rock very fast (in geologic time not human time) – there was little time for those red clasts to get exposed and rounded. Later it was broken up again and transported as a new rock made up of even older angular clasts. Our general classification for this type of rock is called a “breccia” – Google it, you’ll get the full definition and more images. If the clasts inside were rounded, instead of angular, we’d call it a “conglomerate” – both are types of sedimentary rocks. Breccia’s can form is a multitude of geologic conditions and nothing is really diagnostic, but in general they usually represent a high-energy, or tectonic event – something happened to deviate from the normal day-to-day. The clasts are not aligned – some a parallel, some are perpendicular to each other, which add to this interpretation. This is why it appears almost shattered inside. If I had to guess, I think this is a "fault breccia" – again Google this and look at the images. The age of the rock and what geologic formation it came from is the hardest to nail down.
Knowing that it comes from northern Michigan helps a little. Michigan is in the middle of the Michigan Basin, a very big Paleozoic sedimentary basin with old rocks, again Google “Michigan Basin” – think of big giant bowl over 100’s of mines. The middle of Michigan is the high point (center) where the youngest rocks are Jurassic in age (200-145 million years old). As you move N-S-E or W you are getting older and older in age. The northern shore of Superior is Silurian (420-440 million years old) and eventually as you go north into Canada you hit the Precambrian basement or shield terrains which are a couple of billion years old. Since this is a sedimentary rock and contains clasts of older sedimentary rocks, the best you can do to bracket the age as being no older than Cambrian (550 million years old) and even this is poor because it was transported via water, so it could have come from hundreds of miles away.
I have no idea if this is a common local rock and if it has a local name – like the Petoskey stone as an example. Petoskey stones are old limestone chunks that are made up of rugose corals, which have been rounded and weathered on the shorelines, they are Devonian in age (420-360 million years ago). The name is just a local name, not a geologic name. We’d call it something lengthy and confusing and far less interesting than just a “Petoskey stone”.
I hope this helps, I have no real answers and I probably just created more questions, which is all we really do as Geologists - bore you to death on what it's not, but never really tell you what it is.