The best metric of fatness or obesity is body fat percentage adjusted for age.

Reputable sources vary a bit on where they draw the line and at what age. In general anything above 25–30% for men is obese and anything above 20% is overweight.

Ideal Body Fat Percentage Chart: How Lean Should You Be?

US Army Male Body Fat Standards

The US army sets body fat requirements to 20–26% depending on age for men.

“Skinny” is usually referring to a fat free mass index in the lower 10–15% of the subject’s age group.

Fat-free mass index and fat mass index percentiles in Caucasians aged 1898 y

There are people that are both skinny and fat, but they are fairly rare (repeated low protein diets with weight regain and induce that kind of condition).

BMI is an outdated concept that unfortunately is still taught in many medical schools and used by insurance companies. It has some validities for groups, but is a poor indication of individual health outcomes compared to body fat percentage or waist hip ratio.