The Simple BMI is the one which doesn't take the ratio of lean to fat mass into consideration. If you are athletic or muscular it has less value than if you are not.
Obese means you are carrying an unhealthy amount of weight as fat. So a true measure would have to include body fat %.
The reason the Simple BMI exists is it is good as a "general" measure. When I weighed nearly 300 lbs, I would frequently remark that BMI was meaningless without fat % consideration. However I acknowledged that it was probably closer to accurate for me than it would be if I was heavily muscled and athletic.
There are BMI calculations that take body fat % into account, but to make use of them you need some way to reliably measure your body fat%. There are many methods, but discussing them is out of scope for this question.
For the record, I'm an endurance athlete now. I'm 6'2" and weigh 175 lbs with a body fat % hovering around 10%. You do not offend me, but I am not too small by any stretch. I wear size small mens t-shirts but I get funny looks when I say so because I have a long torso and am fairly broad chested. I will acknowledge that I'm not particularly muscular above the waist.