Do all people have the same amount of fat cells?

You're born with a predetermined number of fat cells, with women generally inheriting more than men. The number of fat cells then grows through late childhood and early puberty, after which it is pretty much set. Fat cell number increases more rapidly in obese children than in lean children. The amount of fat someone has is a reflection of both the number and the size of the fat cells.

For a long time, it used to be thought that people got "fat" by filling up those "insidious little sponges," just as you described. It was conventional wisdom that the only difference between obese people and non-obese people was that obese people had all their fat cells "filled up" to maximum capacity. It's now known that we can -- and do, in fact -- "grow" more fat cells in adulthood, and that obese people have more fat cells than non-obese people.

http://www.nytimes.com/2008/05/04/health/04cnd-fat.html