Arnold Schwarzenegger is 6'2" and weighs 257 lbs. Is he obese? Yes! Is he fat? No! Is he more than ideal target weight? Yes. Is ideal target weight the best way to tell if you are in shape? NO!!!
The most disgusting MRI's I ever had the displeasure to see were of the thighs of some young women. Each was well within her ideal target weight, in fact, each was slightly underweight. Each enrolled in a medical study because they had aches and pains, which did not follow any specific diagnosis pattern.
The study included cross sectional MRI's of various body parts. The thigh cross-sections showed that the women had huge fat deposits in their thighs, and elsewhere, and almost no muscle mass anywhere, literally, 3" to 4" of fat surrounding a very small muscle layer.
These women were clearly "obese" even though they did not fit the definition. The muscle to fat ratio was astonishing (sorry, I can't recall the actual numbers).
Now, body fat percentage is a good number to know and understand. It also means something.