Most campgrounds don't have specific tent areas in the midwest. You buy the site based on the amenities of the site, anything from a primitive site with pit toilets and a hand pump well for ~$10 up to a site with full power and water designed for an RV for $30 or more, and any range in between. Not all campgrounds will have all levels of accommodations, as others have mentioned any popular campground is going to be geared towards RVs. DO keep in mind any campground in a popular locale is likely going to be booked months in advanced if it is a holiday weekend, too. On the other side, many of the primitive federal and state campgrounds are set up for local reservation only, on first come first serve basis.

Hiker/biker campsites are commonly mentioned around here, but be aware that they are regional. Camping in Michigan, I have never seen one.

The thing to remember is that in America, you buy a specific campsite, you are not paying a fee to enter an area to setup wherever you want. Therefore, if they are full, they can and often will send you away. That said, it varies wildly on the person taking your money and the actual grounds you are at. I've seen it before on busy weekends where they will try and accommodate tenters, but no guarantees. Also remember that it can be some distance between campgrounds in America.

Many areas explicitly allow wild/dispersed camping. Michigan's rules, for example: DNR - State Forest Campgrounds & Dispersed Camping