Minnesota native who likes to get pizza everywhere he visits, and yes, Minnesota-style is absolutely a thing. Here are the key elements:

1) The crust is incredibly thin. Normally when you think “thin crust pizza”, you’re thinking of that sort of cracker-y, flaky crust you get from places like Pizza Hut, but this is crust so thin that the grease from the cheese and the sauce soaks right through it to create a mildly translucent layer of dough that you can roll up like a cigar with no real effort. (Except for the outer crust, which is extremely minimal—the cheese usually leaves maybe a quarter-inch of a ridge?—but which bakes up like a hard breadstick.) This does make it very messy, because there is nowhere to grab it that’s not greasy. Grab napkins.

2) Cut into squares. This is the thing everyone notices, and so you get a lot of people saying, “But the thin-crust pizza here gets cut into squares, too!” Yes it does but that’s not the only thing.

3) Heavy on the toppings. The cheese is usually pretty generous as well (and usually local), but you’ll always be able to tell a Minnesota-style pizza apart when you order sausage as a topping. You get massive hunks of sausage, usually made right there in the restaurant, easily worth eating by themselves. (The first time my wife had Minnesota-style pizza, she went from “huh, is that a thing?” to asking the restaurant if she could buy the sausage from them for her morning omelets.)

4) Lots of sauce. I’ll be honest, I don’t generally notice a spicier sauce than usual, but I do notice that it’s spread on pretty thickly. If you bite into it and you get sauce squirting onto your fingers, you’re eating Minnesota pizza.

I have also heard this as “Midwestern-style pizza”, so it’s probably proliferated into the surrounding states, but it’s very clearly different from New York and Chicago style. I will say that if you’re going to be in the Twin Cities, skip Red’s (the owner is a racist fuck) and go to Broadway Pizza or Carbone’s Pizza. Both will give you the distinctive experience.