What you’re describing sounds like normal camping, you hike for a few hours and pitch your tent somewhere. Isn’t the drive in picnic variety just an American phenomenon?
I'd be fascinated to know where you live that "hike for a few hours and pitch your tent somewhere" is normalized and the very idea of a camp site sounds foreign.
But what shocked me in the US was that there are "nature" camp sites where you more or less drive up to a designated, single tent spot where you pitch your tent. It's baffling and seems to entirely defeat the purpose of camping in nature.
When my SO and I did a multi-week cross-country trip we went for whatever designated camping sites was close by and pitched our tent there (except Berlin, there we went for a Airbnb). Though for us this mostly replaced switching hotels every other day. We then did local stuff around there, like canoeing, hikes, museums,... However, we did spent some nights in the wild, with camp beds (US: cots) placed next to the car. But when you don't know the general area, finding a good spot for that proved rather difficult. Entering forests with a car is usually verboten, and close to main roads there will at least be a lot of morning traffic; OTOH we had a pleasant conversation with some elder locals on a morning hike when we found a spot near a nice fishing pond in a small forest (yes, yes, driving there was erlaubt, not verboten). They only regretted not having some coffee for us :)
If you're considering going to Scotland and are thinking of that sort of thing, you should also look up the concept of a "Bothy" or "Bothies", which tend to be in mountains. They are a sort of refuge/simple transient accommodation. Generally small, quite basic huts in the deep countryside and remote places, where you can stay without booking and for free, but just overnight while you're on your way around.
I'm not saying you shouldn't put your tent on a crowded lawn, or next to your car, if that's you want to, but it obviously doesn't serve the same purpose as hiking up the mountains and putting your tent next to a brook, miles away from anyone else.
> lots of people enjoy being in more or less wild nature
> camping [is] about self-sufficiency and simplicity
There's usually some sort of toilet facility.
I'm not aware of fully 'wild' camping here, and you'd want to pick your spot carefully because of the crocs and snakes. Not that they're fully absent from the marked places!
What you're describing sounds like a modern 'soft' version.