Yes, you are correct: these veggies have nothing in common except that they are difficult to categorize and therefore have been given their own category.
Although they have a couple of things in common: you can eat both corn and mushrooms raw, although we tend not to (you should though, if you get really fresh sweet summer corn). They're both delicious cooked very simply, with a bit of olive oil or butter and maybe some fresh herbs. They're also both good roasted or grilled, with a bit of char. And both corn and mushrooms can go in lots of different dishes. Check out some options below: