As a society, we are fat phobic. This means that all of us face or deal with fat phobia in one way or another. It's so bad that we have potato chips that actually include ingredients that our bodies cannot digest. On the other hand, fat oppression only affects a select group of people in our society.
Fat oppression is spawned out of people's fear of fat.
All of this is a form of oppression, but not everyone suffers from this oppresion - only fat people and in particular, fat women. Fat phobia and fat oppression are clearly different from each other. They are also connected in a very important way. Phobia make oppression possible. The way in which our society is constructed, makes our fat phobia invisible, hence fat oppression is still one of the remaining legitimate, acceptable, and legal forms of discrimination.