The words “fat” and “Skinny” are both a matter of opinion. There is no quantifiable way to determine when a person is considered “fat” to all people. It's the same with “skinny”.

Underweight, overweight, obese and morbidly obese all have quantifiable ways to determine if a person meets the medical definition. Some of the ways they can be determined is by measuring body fat, estimating body fat (like with BMI) or waist size relative to height, or hip size.

As far as “skinny”, it is defined as “very thin”. To one person a person of a normal weight is very thin, while to another it is someone that is a very low, or underweight.

Some children think their chubby classmates are “fat” while their parents think they are normal. Some adults think anyone that is classified as overweight is fat, while some adults don't think a person is fat until they are morbidly obese.