It seems that there are many definitions of quasi coherent sheaves(modules). There is a nice page on nLab quasi coherent sheaves
My questions are:
Are there any other definitions of quasi coherent sheaves? For what?(I mean in which situation, they should be redefined to satisfy the working environment)
How are they related?
For question 2, nLab says these definitions are equivalent. There are four definitions in nLab. It seems except first definitions, the other three are equivalent, just restate in different language: i.e presheaves <---> pseudo functors <---> fibered categories.
But are these definitions exactly the same as the classical definitions? (as locally presentable modules)