If you've gone for a hike in the bush, and you come out anywhere other than where you intended to be . . . you were lost!
That would be my definition of "turned around". Lost is you don't know where you are, you don't know how to get back from where you started, and you can't figure out which way to go to get out.
I've wound up in places I didn't want to be ( how the hell did I get HERE!), missed the trail I was looking for and had to cut cross-country, been disoriented by thick bush or heavy snow, but I've never been so lost (knock on wood) that I've had to spend the night or someone had to come and find me. That's not because I have a homing pigeon's sense of direction, it's because I carry a good compass, religiously.
I prefer to regard the term "turned around" synonymously with the word lost. This mindset might prevent me from making bad decisions that could have serious consequences. For example, we have Hudson Bay to the north and east, and the rail line runs south from town, so if you're east of town, the only "wrong" direction, provided you travel in a straight line, is south. If I got turned around, regardless of the reason, and headed south, how many days would pass before I admitted I was lost, or until I hit the Nelson River, 100 miles away. In reality of course, if you traveled a couple of hours without coming across a familiar landmark, you'd probably realize you had a problem. Yet you'd know there was sea water to the north and east and a rail line to the west, so its not that you don't know where you are relative to major landmarks.