Usually backcountry camping requires hiking in to a site, whereas "tent" camping would refer to stays in frontcountry campgrounds that are usually accessible via a car. With exceptions, tent camping would require a reservation, whereas backcountry camping sites often are occupied on a first-come first-served basis.
Tent camping: a flat spot, maybe a picnic table, one parking space, an elevated grill, a water spigot, on-site trash facilities, and a common toilet/shower building. The extent of your assigned site may be lined with old railroad ties, and clearly labeled with a numeric sign.
Backcountry camping: a flat spot, a firepit ring, a covered latrine pit with a park service logo on it, and a cable on a pulley for your bear bag. The extent of your site might be represented by a dot at a place on your topo map that slightly differs from reality.
Some tent campgrounds also offer wi-fi and limited electrical power distribution.
Most of the backcountry camping I’ve done in the US has been “find somewhere 1-2 miles from any formal trail” and you’re on your own. No signage, no toilet, no nothing. Usually only fuel fires and no fire rings (especially in the west).
National forests are usually like you described, but most national parks have camping areas with toilets and bear lines available at popular backcountry locations. Most national parks also allow dispersed camping, but not all - Rainier for example requires reservations for a particular campsite.
This is a subset usually referred to as dispersed camping. IME, this is usually the case in US national forests (in fact, I think the rule is that it is allowed by default).
There are a number of parks (including most US national parks) that only allow backcountry camping at designated sites (which may or may not have the amenities described by the GP).
OK. I've only formally backcountry camped in Arches (mile from any trail - no amenities or sign of previous camping where we were), Yosemite (we quietly camped on top of Clouds Rest so obviously no amenities), Joshua Tree (off trail, random spot with amenities), Canyonlands (Needles in a designated spot but no facilities just a marker, and Maze in a random spot with no indication of previous camping), and a few monuments/areas (Coyote and Buckskin Gulch, etc).
To me, "back country" can mean many things, down to no trail and essentially no services. For example, when we backpacked in Denali many years ago, all we had for toilets were the shovels and biodegradable toilet paper we brought. Very different from camping next to your car and having a restroom with running water nearby.
